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.
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.