I'm trying to say "blessed with many talents", but I am not sure if I am using たくさん correctly here. I am thinking that 「たくさんの才能に恵まれている」 is more grammatically correct but I can't think why. Maybe because たくさん is both an adjective and an adverb, and thus whilst 「たくさん飲んだ」(drank a lot) makes sense, 「たくさん恵まれている」(be blessed a lot) doesn't sound so natural.
I haven't seen that exact phrase, but I have seen 「多くの才能に恵まれている」, which is basically the same thing, just a different word for "Many". See here for a discussion on 「たくさん」vs「多い」: Usage of たくさん vs. 多い. They discuss the adverb-adjective issue that you mentioned.
I agree with Halfway Dillitante. 多くの才能に恵まれている sounds right. You can also say 才能にとても恵まれている or たくさんの才能に恵まれている.
Yes, I know why you used たくさん. It can be used as an adjective.
However, たくさん恵む somehow sounds unnatural. It's grammatically correct. But still strange. I don't know why. Maybe it's a collocation.