Yes but it will be very expensive (like .50 a text and $3 a minute to talk). Need to call Verizon and get an international calling package that will help some with the charges.
If you are staying for a long time best to call Verizon tell them you are leaving the country for extended vacation and ask them to unlock the SIM. That way when you get to Belize you can get a local SIM card and use the local network.
Don't take no for an answer. They CAN unlock the SIM you just have to get the right person on the phone.
I used my Verizon phone in January and ended up costing me a $2400 phone bill
inbound text messages with Verizon are .20ea and outbound .25ea ($US). I usually tell my staff to text in emergency/hi pri situations only and I will most likely respond via email. Otherwise, contact me via email (that I might check every 2 days )
You need to check the type of phone you have with Verizon to be sure they have a SIM card if you want to switch it out for a local one. Verizon sells iphone 5's factory unlocked and have a sim... 4 and older do not. Not sure about other types of phones they sell.