No, Super Mario Bros. Special was a licensed game, unlike The Great Gianna Sisters (which was made in 1987, where SMBS was 1986). As far as I know, hacks aside, it was never turned into a Mario game, as I have never played a Mario game with those level designs, and even if they made one with those level designs, it would be considered just close enough to be an absolute ripoff. Also I haven't seen the powerups of the game in any Mario games, or certain enemies.
In conclusion, etc.