9 speed derailleur on 7 speed cassette?
Yes, all 9-speed Shimano rear derailers share the same actuation ratio as all Shimano 7-speed ones,  except for pre-7700 Dura Ace.

I've never seen a 7-speed chain rub inside a 9-speed RD cage. If somehow that were an issue, an 8-speed chain would work fine.