What happens (if anything) when installing non-free app in Replicant?

[Advrk Aplmrkt]

Hello,
If I setup Replicant on an officially supported phone, but need to use
a couple apps that are currently unavailable in the Replicant app
store, and obtain them from elsewhere, would I be able to install them
anyway?
For example, I am looking for a good CardDAV contacts sync app but
have not found one in the Replicant app reposotory, so might want to
look for one in the Android Marketplace. If I find one would it work?
Thanks.