Sprint is CDMA, ATT is GSM. Sprint's SIM slot is unlocked only for international carriers. US Carriers don't unlock their SIM card for use with other US Carriers.
Only the GSM-compatible iPhone is sold unlocked through Apple. You can't take a Sprint iPhone and put it on the AT&T network because it's CDMA and the Sim slot is restricted. There is no "unlocked" CDMA iPhone.
So, no, you can't do this.