The long answer includes explanations as to why the answer is usually no and can be read below.
Aftermarket or over-the-counter (OTC) oil additives come in a few general variations:
Performance Additives Viscosity Modifiers Cleaners Inhibitors Magic & Sci-Fi There can certainly be other types, but a vast majority of OTC additives fall into one of these categories.
Performance additives generally include anti-wear, extreme pressure, and friction modifying additives. They often have some root in traditional oil formulations; meaning they are commonly used in existing oil formulations and advertised as "performance boosters". For the most part, as OTC additives, they are unpredictable at best, the marketing claims for their performance is rarely supported by any credible evidence, and they usually don't live up to the expectations.
A big problem is: more rarely equals better for these additives, and simply adding them does not increase the advertised performance reliably. Many of these types of additives experience diminishing returns with regard to performance and their proportion of the lubricant formula. Other groups of them actually experience decreased performance with increased concentrations. So adding them to oils that already have additives providing this performance results in neither additive groups doing the job right.
Another problem with these additives is their ability to disrupt the surface activity the additives of the original lubricant were designed to do. So by adding one of these chemicals, it is likely to diminish the original performance of the lubricant and substitute it with a potentially less effective replacement.
There are undoubtedly many anecdotes of these types of additives doing good, but that is more than likely due to either luck or a placebo effect. Every oil formula is different and adding these random amount of random additives is unpredictable at best without knowing the original oil formulation and exactly what you are adding at what quantity. No additive I have ever come across would work in every formula at the exact same concentration.
Viscosity modifiers are typically either high viscosity oil or a polymeric fluid. They are usually un-additized and therefore dilute the original lubricant's additive concentration. This is bad for similar reasons stated above regarding changing the additive concentrations. By changing the formula concentrations, you may be changing performance aspects that were balanced in the original formula to an unbalanced concentration. These additives can be useful in a few circumstances though. They can be temporary fixes to compression issues and leaks, but even in fixing those problems, you may introduce unintended consequences such as engine efficiency and oil supply through the pump. If it is the only way to get the bike somewhere for maintenance, it might be the best option, but still not good for normal use.
Polymer fluids in motorcycles add an increased risk. The increase in viscosity is usually very temporary because these polymers are not often shear stable. So once they shear, you have no increase in viscosity and a diluted bulk of oil. So it is a lose-lose in that situation.
Cleaners come in two main varieties: detergent/dispersant additives and flushing compounds.
Detergents and dispersants are similar to the performance additives in the sense that they are very surface active and can disrupt the surface active additives of the original oil to its detriment. Detergents, dispersants, anti-wear, and friction modifiers are carefully balanced in oil formulas and increasing the detergent concentration can prevent those other additives from interacting with the metal surfaces where they normally would. Generally speaking, unless you have an engine in absolutely terrible shape, with regard to sludge and carbon deposits, a good oil already has more than enough of these additives in it to do the job.
Flushing compounds are usually some sort of high solvency fluid meant to dissolve sludge and carbon deposits in dirty engines. These can be useful in very dirty and neglected engines as long as care is taken not to overdo it. If an engine has a high level of sludge and deposits, it is possible to release too much all at once and cause unintended harm by blocking oil flow or forcing that bulk of contaminants into areas it can do harm. So an engine flush can be useful, but care should be taken when doing so.
Inhibitors usually take the form of antioxidants. These are safer than some other additive types because they aren't generally surface active chemicals. They do still dilute the overall additive concentration somewhat and can possibly throw off the balance of a formula to produce worse overall performance though. There is less risk in using these types, but still, your typical oil should have more than enough antioxidant additives in it to begin with and there is rarely a need for more to be added.
One final thing I'll cover here is the "magic" and "sci-fi" group of additives. These are the types that usually make some pretty unbelievable claims. They are usually unbelievable for a reason; because they are nonsense. The claims by the "manufacturers" (usually marketers, not chemical manufacturers) are very lofty, always unproven and supported by anecdotes, and typically backed up by lots of buzz words and little substance in any true technical sense.
Typical claims are:
large increases in power and efficiency rebuilding of metal surfaces from the inside out fixing leaks with no effect on any other property of the oil "nano" (This prefix above all other things makes me cringe and look closer at marketing claims. Yes I will admit I am prejudiced against "nano" materials in lubricants, but I will also be the first to admit it when I see one that is proven to actually work as advertised.) Typical results are:
nothing harm benefits claimed with zero evidence lighter wallet and again, nothing For a motorcycle with a wet clutch, one thing to especially look out for with any additives is whether it will affect the clutch. Some additives are right up front with it and say not to use it with a wet clutch, but others are less obvious.
So in summary, yes there are a few circumstances where benefit can be had from using an OTC additive. In most cases though, there's not much to gain and they either result in a performance decrease or no change at all.