I think it's the exact opposite, as they operate on a token-level, not a character level, which makes tasks like these harder for them. So they would generate a sentence with multiple es in it and just proclaim that they didn't.
(Just tried it, "write a short story of 12 sentences without one occurence of the letter e" - it had 5 es.)
(Just tried it, "write a short story of 12 sentences without one occurence of the letter e" - it had 5 es.)