Can a customized or non-bitcoin node be made to talk to a bitcoin node?
Of course.
Bitcoin nodes are just software that implements the Bitcoin P2P protocol. There are many software packages out there that do so (including full nodes, standalone wallets, indexing software, ...). There is no magic sauce that somehow blesses a particular piece of software into the realm of nodes - anything that speaks the protocol will do.
Furthermore, most of these (and probably all the ones you should care about) are open source, so making modifications to add functionality yourself is very much possible.