I'd say "perhaps," but I can't really answer the question. It may be a good idea for you to come up with some examples of when you want to use it (医者的, 家的, 提案的, etc.) and see if they pass the grammaticality test. I can't really say whether it's reasonable or not that you can just add it onto the usual na-adjectives we learn as standard (although I have to say, I don't know what those are).
However, I have read that there seem to be lots of instances of people say things lately like watashi-teki ni... or kurashi-teki ni... or jikan-teki ni..., and these are considered bad style, and the impression that the speaker can't speak their minds in a straightforward manner can be taken away from it.* So the answer to your question may be "yes, but there's a stigma involved." But that may just be older people thinking that about young people's speech, or it may have changed since 2004, when my reference was printed.
*[Source] 問題な日本語