If, and this is a big if, it can support an RSS feed that also allows you to provide the requisite info apple et al demand (3000x3000 pixel image, categories, etc.) then it could in theory support it. The bigger concern is traffic - will they be cool with you syndicating out and having folks pulling that frequently and can it support a lot of folks with larger shows doing it. Some podcatchers won't care and will let you just use an RSS pointing at the page hosting the files, but it's not a given especially with the larger ones.

My advice? Unless you want to really hack it together yourself and accept that it could force you to migrate without any notice, sure give it a shot. If you are risk averse, don't want to disrupt your listeners, aren't really comfortable doing a lot of tech troubleshooting, etc. I'd say don't try it. Podcast hosting is trivially inexpensive and all the big services have an embeddable player now if you really want folks to listen on your site.

Edit: worth noting that a lot of this is going to depend on whether an instance admin specifically wants to deal with all your traffic, assuming you get regular users/the numbers are decently high. If you stand up your own instance then it's all about what your infrastructure can support.