No, this won't work. Plecos don't eat garbage: they're often thought of as 'cleaner fish' because some species will conveniently eat algae and leftovers, and because they tend to be pretty inconspicuous, but none of them will thrive for long on detritus. The muck in your filter media is a mix of rotting food, fish poop, and bacterial growth. Even if they could clean it out completely, it wouldn't be a healthy diet for them.
There are hundreds of species of plecos (or, more formally, loricarids) and they all have particular diets composed of plant matter, microorganisms, meat, and even driftwood. And naturally, a diet that works for one species may not work for another. You probably have what was sold as a common pleco, which likely to be Pterygoplichthys pardalis, but could be one of several similar species. All the fish sold by this name are omnivorous, and as grazers which a need to eat nearly constantly, they tend to eat a lot of plant matter -- they'll eat algae when they're young, but they benefit from blanched vegetables like squash or zucchini, and that type of plant matter becomes more important in their diet as they grow.
(As a warning, anything sold as a 'common pleco' will outgrow your 15 gallon tank and then some; they can grow to about two feet long, and even when relatively small are high-capacity poop machines that will overload a small tank's filtration. My frank opinion is that these plecos are not really suitable for most home aquaria.)
Some filter media can be easily rinsed off with some light hosing, by the way -- though you have to be careful to not kill your biofilter when you do this, of course. A lot of hang-on filters don't have what look to me like very durable media cartridges, but sponge and canister filters are designed to be cleaned and reused.