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?
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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.