Yes.
Moreover the position is obviously legal.
btw, i count (46) ways a queen can check w/out making a checkmate or stalemate. multiply this by alot and u have 100's a moves before u make a 3-fold repetition. the 50-move rule will apply here as there will be NO pieces removed from the board.
so, draw in 50.
Actually, you can go far further than 50 and you can allow capture without checkmating or stalemating. You can go further than I do before offering the capture, I just don't wish to type that much. It simply proves the point that you can go beyond 50.
1...Qe8d8+ 2.Kc1 Qdc8+ 3.Kd1 Qcd7+ 4.Kc1 Qdc7+ 5.Kd1 Qcd6+ 6.Kc1 Qdc5+ 7.Kd1 Qcd5+ 8.Kc1 Qdc6+ 9.Kd1 Qce8 10.Kc1 Qb8c8+ 11.Kd1 Qc1+ (you can go further - I refuse to type that much) 12.Kxd1 (50 move count resets) Qe8d8+ 13.Kc1 Qdc8+ 14.Kd1 etc.
Forget 9 Queens, here is 33 queens, and with black to move there is no stalemate.
I already got 47 queens no stalemate.
It'd need to be a rigged game for sure.