Nope there’s only one, and it’s located in a room in World 3-3. (And oddly the manual showed the red Snifit in a different area.) Never understood why they used it only once.
 
Also that sounds like a cool SMB2 homage if that is the only red parasprite.  
I don’t get why SMB2 gets some “hate” online honestly, it was a great game even if it wasn’t a “real” Mario game. But hey “Doki Doki Panic” the game it originally was based off of, was made by Shigeru Miyamoto, and the same people who make the Mario games, they apparently don’t know.

I could have sworn there was more than one red Snifit, but I haven’t played Super Mario 2 in about 6 years.

I surprised they didn’t use the Red Snifit more than once.

Coincidence?  
I think MAYBE!