I want to keep my Alltel plan but use a Verizon phone with it instead of an Alltel phone. Is this possible?

yes in fact all cell companies share the same cell cites.
some parts of New Mexico are exclusive and you get a message, it will ask for your credit card as you are roaming and will cost maybe $2 or $3 a minutes.
if you ever get that message and you must make the call be forwarned. if not necessary hang upp