No. Firstly because it is spelled “typo.” Secondly you typically use the diaeresis to tell the reader to not confuse it with a similarly spelled sound or diphthong. So it tells a reader that “reëlect” is not pronounced REEL-ect, “coöperate” is not COOP-uh-ray-t, and “naïve” is not NAY-v.

Because written English makes so much sense normally. God forbid someone has to figure out the ambiguous pronunciation of those particular words. It seems like a silly thing to provide extra guidance on to me.