First, I would be careful with such linear thinking. Oxygen (triplet) reacts with hydrocarbons (singlets) all the time to form two singlet state products - combustion. The thing is that spin-balancing of a photophysical or photochemical process doesn't determine whether a reaction will happen; rather it determines the favorability (rate, say) of a process. An excited triplet chromophore will eventually decay back down to a singlet ground state even though it's a spin-forbidden process. The presence of a ground-state triplet (oxygen) can make this process occur near instantaneously via energy transfer. Some metal polypyridyl complexes have excited triplet lifetimes on the order of tens to hundreds of microseconds in deoxygenated solution. In the presence of oxygen, that lifetime goes down to about 1 microsecond - and this is only limited by the diffusion timescale of oxygen in solution. Note that the absolute rater of a process depends on a lot of factors. The rates of nominally spin-forbidden processes can differ by many orders of magnitude, from sub-microsecond to greater than second timescales. So, it is important not to oversimplify. Particularly in the case of chemical reactions (versus photophysical processes) that have additional complicating factors - diffusion rates being one of them. For a biomolecular reaction giving 1 or 3 products... this complicates things even further. I don't know if I'd feel comfortable trying to generalize expected results. Did you have a specific example in mind.
Bear in mind, also, that there are very few common molecules that have stable radicals or triplet states. Oxygen is very unique in this regard. Even in the case that triplet oxygen can sensitize the production of another triplet-state species, it is likely this product will relax eventually to a singlet (and singlet oxygen will relax back to a triplet by physical or chemical routes). So you have to consider what the downstream products are as well.