If you really over fertilize, then yes, definitely. Some fertilizers contain high salt content and most contain enough nitrogen to burn plants if you apply too much of it. But it would take a lot of over fertilizing to kill a strong palm, especially one of a mature age. Over fertilizing will slow the growth of most plants so definitely make sure you arent feeding too much.
-Alex

All of my palms have leaf tip burn, which now I know is because of my lack of knowledge when it comes to fertilizing palm trees. If I water them again without fertilizer will I be able to sort of dilute what I put in them?