Do you put a comma around "as well"

If you put the dependent clause in the middle of the sentence like that (between subject and action), then you would "need" to couch it in commas to set it off from the rest of the phrase, and because you would pause there, anyway (read it out loud).

If you moved that modifier -- it's almost like an adverb, come to think of it ["as" definitely is] -- to the end of the sentence, you would only need one to set it off.

He no longer held the need to impress her, as well.

But then you have to be careful with the semantics in context, and make sure that the sentence before doesn't make it ambiguous -- indeed, reducing ambiguity would be the strongest argument to jam it as close to the subject as possible, commas be damned.