Yep, definitely. And not just because of the eyes. They have the same body and head structure, and same voice actor for the English, French, and ( I think) the Korean dub. their facial structure is also similar, if not the same. Not to mention, Gabriel isn't ever around, and has only appeared as the same time as Hawkmoth in the Simon Says episode.
Gabriel and Hawkmoth both have the same ring, on the finger and hand(can't remember where though). Also, in rhe Origins episode, we see a picture of Adrien's Mother- Gabriel's wife in the brooch of Nooroo that belongs to Hawkmoth. And the windows in the dark room Hawkmoth sends his Akumas off, look very much like the windows in Adrien's mansion somewhere (I think to the side or the front).