It should work, that is after all the entire point of SIM cards, so that users can swap phones whenever they want.
If you lived here in Europe I could guarantee 100% that it would work. I do it all the time, I have one SIM card between half a dozen phones and never have any problems.
Unfortunately the sometimes rather awful people who operate phone networks in North America seem to put in all kinds of dirty tricks to try and absolutely control everything their users do.
Why don't you just buy SIM-free phones? EDIT: Sorry that was a stupid question, I'll try reading the post next time. :-)