Interesting. The English Wikipedia page of Major Havoc says

> Although Major Havoc was not a major commercial success in the West, it had a significant impact on the development of the Japanese computer game industry.

The Japanese Wikipedia page mentions four games which are influenced by Major Havoc, though they don't say anything about Super Mario Bros. The earliest listed game is Theseus (1984) for the MSX, which basically copied the Major Havoc platforming physics. It's also possible that this one influenced Super Mario Bros (1985) rather than Major Havoc directly.

Though it is worth mentioning that these games apparently had unlimited upward acceleration from holding the jump button (kind of like a jet pack) and they had a head bumping mechanic which would let the player drop down stunned. SMB didn't have that.