No, you have to lift the rook as well!
Bulldog Chess with Spy- HolographWars vs. rychessmaster1 (unrated- Spy test game)

I dunno, but if you didn't, that may lead to repetition. The Spy in general could easily lead to repetition, with the Queen moving and the Spy chasing it.

So is it or is it not necessary to keep the Spy in the Rook? Personally, I think not. That would mean committing a piece to death, all for the enemy Queen. What happens in the event of a Queen trade? Your Spy, and the piece it inhabits, are useless.
Position after 6. Qf2 Sj8 7. e3 Ng6 8. Nxf5 SRj6 9. Nxd6 Sxf2