I can’t imagine why it wouldn’t work. Dura Ace 8 speed shifters were the last series that had the funky cable pull requiring being paired with a matching rear derailleur. The 7700 nine speed series should be compatible with other Shimano 9 speed rear derailleurs.

The only potential incompatibility that I can think of might be along the lines of the current Tiagra 10 speed 47xx series that appears to use the current 11 speed pull rear derailleur. Hopefully someone who has used the Sora 3500 series can pipe in here...