That depends.
Some things to consider:
Most importantly, is this a Sprint iPhone? If it's not, it doesn't matter. Sprint won't activate it. It's their policy never to activate any phone (iPhone or not) that was not originally intended for their network.
If it is a Sprint iPhone, does it have a clean ESN? If it doesn't, then Sprint won't activate it. The ESN/IMEI is specific to the device and not the SIM card.
A SIM card is bascially a chip that allows you to use different networks. Sprint only allows a non-Sprint SIM card to be used in their devices for international use, i.e. it's unlocked for international use. The SIM card that is in that iPhone will need to be a Sprint SIM card if you want to use it on Sprint's network. It follows then that the iPhone will need to be a Sprint iPhone.
If you have a Sprint iPhone and a Sprint SIM card and the ESN on the iPhone is clean then you should not have any issue activating the iPhone. If any of these are a problem then Sprint can't activate the iPhone for you.