As mentioned in this Meta question, approval of an edit suggestion gives the suggester +2 reputation.
If the suggestion is rejected, does it cost the suggester any rep?
No, but repeated edit suggestion rejections from multiple users will cause your edit suggestion rights to be suspended for (n) days, where n is currently 7.
Note that after a recent change, automatic rejections due to edit conflicts are ignored and won't affect the suggested edit ban mechanism. (only rejections made by actual users)
I have no facts backing up this answer but, doing so would be incredible stupid as it would discourage people from trying to make SE a better place.
And since the SE team make 84.76% more good decisions than bad I'm betting the answer is no.