Or can I just spam them out as fast as my program can send them, as, like you said, you cache it anyway.
No. The throttle discussion page specifically says:
... we consider > 30 request/sec per IP to be very abusive and thus cut the requests off very harshly.
See also: ["Is it possible to access data in real-time using the Stack Exchange API?"][2]. Once per minute is a pretty reasonable rate to repeat the same request. Multiple times per minute also risks running out of quota -- especially if you make several calls per batch/poll.