Not a good idea, for all the reasons mentioned above.
As a push-up, it’s not all that effective.
As cardio, it’s also not all that effective.
So, I guess if you’re tired and you need to rest, and you’re not concerned that the push-up won’t be that effective, and you’re not worried about the risk of falling off the bike, it’s fine. IMO, get off the bike sooner and include a weight training session afterwards if you really want to work your chest. Since the posture is already hunched over in spin anyway, if you’re going to get off the bike and weight train, work the middle back! 😀