Nope, SMB1 was a smash up. SMB2 was made by folks that had no idea what they were doing so SMB3 went back to basics. I very much remember the sequence of events. Mario Bro's (and Donkey Kong) were games on the Famicom in Japan that were decent. The issue was with Arcade's in Japan making more money than home systems so they introduced the Nintendo VS cabinets. This helped but it wasn't enough and so in 1985 they greenlit the Super Mario Bros proposal while dealing with the NA launch and the NYC event. Shigeru Miyamoto carried the development and he deserves the credit but corporate was throwing shit at the fan and seeing what sticked. He just so happened to have a plan that required less work from creative.

Any links to read more about this?