Can you get an unlocked iPad 3G or 4G, put a Sprint SIM into it, and use it on the Sprint network? I'd be willing to pay for the service of course, but really want an iPad without changing carriers.
Yes, no, and no.
What you could do is purchase a mobile hot-spot from Sprint (with no contract) and buy data by the month. You'll save some bucks by only having to buy a WiFi iPad and buy data only when you need it.
You could also buy a mobile broadband plan (tethering) for your smartphone and still only have to buy a WiFi iPad.