While a ship is in port they usually turn off their own towers to allow you to roam off landbased towers. So yes, watching that ERI banner will let you know if you're on Verizon Wireless or Extended. However, if you're in Alaska you're roaming on extended networks anyway. So it may be difficult to tell. You're best bet is to make sure you're physically on land before using your phone.
But texting while on the cruise ship and using their towers is .50 to send and .05 to receive.