YES !!!!!
When I upgraded my phone a few months ago on AT&T... I had to activate a new Sim Card with the new phone... but my phone was defective and had to be sent back. I was told by a Rep to just pull out the New Sim Card and stick it into my old one until my replacement arrived. And YES, it work. Also, when I went online to check my account, it even showed the current (my old phone I went back too) phone the card was plugged into...
Also, many people have multiple phones and a single SIM card and switch phones all the time while using the same account. So it's ok... You would be good.