Please see this thread:
It shows the different versions of the P7 for use in different countries.
I don't think it will work at all on Sprint, as Sprint is a CDMA network.
Also -- again -- My understanding -- is that the Chinese CDMA (TD-SCDMA) is an entirely and completely different thing (different frequencies, different protocols) than the US Sprint/Verizon CDMA. The P7-L00 would not have 4G at all (and spotty or no 3G) in the US.
For the P7-L10 ("International Version") it would work as follows:
It will work as a basic 2G phone on AT&T or T-Mobile in the US.
It should work on AT&T or T-Mobile 3G in some areas, but since it is only quad band - (No 850MHz band - Not penta band) it may not work in all areas.
4G LTE will not work on AT&T or T-Mobile, or on any provider I know of in the US.
AT&T uses Band 17(700Mhz), Band 5(850Mhz), Band 2(1900Mhz), Band 4(1700/2100Mhz)
T-Mobile uses (apparently) only Band 4(1700/2100Mhz)
The P7-L10 uses LTE: B1/B3/B7/B8/B20
No overlap means no 4G at all.
There is supposed to be a P7-L16 international version that may have different 3G/4G bands, but apparently it has not shipped yet, or at least I do not know where to buy one.
Note, however that it does have WiFi, so as long as you do not mind paying a premium for 4G LTE that will not work at all, you'll have plenty of data connectivity as long as you have WiFi available.
Hope that this helps. This is what I have found in my research, as I would really like to buy one of these phones, but as mentioned, I cannot see paying the price these phones sell for, and then have no 4G at all.
Those in the know, or who have one in the US, please comment/correct.