No. Not yet at least.
It is hard for a guy with six years as a starter to surpass someone who played for 15-plus years.
However...he does have a shot at it. He is probably the only active QB capable of surpassing guys like Peyton and Montana and Brady (source: my opinion).
The thing is....it is very obvious that he is very talented AND cold. He plays with the arm talent of Dan Marino, the inteligence of a seasoned QB and the coldness of Tom Brady. Oh, and he can run too. There is no Allen/Burrow vs Mahomes = Manning vs Brady talks going on because Mahomes is BOTH Manning AND Brady. He is THE most talented, the best pure QB, AND the best winner, the coldest in the league today.
If we were talking about 7 years carrers...yeah he is pretty much over anyone. But to be the best ever he will have to keep going like this for at least 5+ years, win about 5 SB (total) and a couple more MVPs.