In my opinion, it would sound a little comical. :) The longer form (mnie, tobie...) is typically used where "semantic stress" is to be put. In the example above the sentence focuses on (why) the keys are being given rather than who they are being given to.
Mnie dajesz klucze - you're giving the keys to me (But you need to think about it as if it said "I am the one you're giving the keys to") To emphasize the word "mnie" even more, you can say "To mnie dajesz klucze".
Also/therefore, it's advised not to use the shorter form at the beginning of a sentence.