I suppose it's possible. The amount of absorption is going to depend on what specifically is 'in there.' Most vitamins (for example) have been separated from their pre-eaten location/environment by the physical mastication, churning, and compression; and by chemical means by chelation agents, acid/enzyme digestion, or other molecules that break apart lipid blobs and such; and even more importantly, are done in areas designed for absorption with lots of villi to give a million times the surface area. Alcohol, the oft-given example of a substance absorbed by the rear part of your gastric tube, is a fairly 'ready to be absorbed' compound. Suppositories are also similarly in a state that makes their active agents easily absorbed.

A whole bananal probably is going to be absorbed like a rock through a 5mm sieve. The bacteria in the rectum might start the process, breaking down the cells and matrix of the banana into readily absorbed compounds, but if you've ever seen an organic object like an apple or banana rot outside somewhere, it is a very slow process. You'll be much more likely to suffer some form of infection/sepsis from the bloom of bacteria (or the smaller chance of a fungal infection) long before enough of the banana is absorbed.

All of this is even more true if the OP was shoving them still in their skins in. The bananal skin will definitely be a very slow degradation, and absorb like an intelligent thought into the president elect.