"멘트가 조~금 감동적이긴 하네"

Yes, it sounds a little sarcastic because of 조~금 and the -긴 하네 ending.

조금(a little) already makes light of of whatever was said, and the "~" symbol (for drawan-out speech) adds a playful derision.

-긴 하다 (-기는 하다) is like "(It) is somewhat (that way)", or "You can't say it is not so", as if grudgingly acknowledging something.

So the sentence is like saying:  The comment/announcement might be called somewhat moving (if I be generous).