I've tried it with snatches and power pushup, and with double cleans and power pushups. I would not recommend it.
I have done a lot of 044 snatching, and separate 044 power pushups (each exercise in a separate session or on a separate day), and it's one of my favorite protocols, but I just don't think snatches and pushups play well together when combined.
Snatches or double cleans and power pushups was just too much local muscular fatigue in the delts and triceps. The pushups didn't affect the snatches so much, but the snatches significantly reduced my ability to maintain power in the power pushups. However, in terms of breathing and heart rate, the recovery was easier alternating exercises.
If you can do it, I would question whether you are going heavy enough or being powerful enough or using a high enough cadence on your snatches, and/or whether you are doing the pushups with adequate power and/or adequate resistance. Power pushups should be a free fall down ("playing chicken with the floor") and exploding up, with elbows tucked in. I try to keep my sets to 9 or 10 seconds (10/2). If it takes me 11 seconds for two sets in a row, I'm done for the day. If you can easily and consistently crank out 9 second sets for 5 or 6 series, it's time to add resistance.
There's also no way I could do 033 timing with just snatches. If I could, I'd know my bell is too light or I'm holding back too much. If you feel like 044 is too much rest with snatches, go heavier or increase the reps higher than 10/2, such as 15/2 (yes, this option is in the book). After two series of 15/2 with a suitably heavy bell, you will be sucking wind through every hole you can get it in, and be thanking Pavel for that extra minute of rest before series 3, if you're not already tapping out at that point.