Yes, of course. As long as you have access to the internet, your VoIP phone system can follow you.
Two of the top advantages of having a hosted VoIP service is the portability and cost. You can continue to take calls via smartphone, laptop, or even an analog phone if you have the right adapter/router.
Some countries may restrict SIP-based internet traffic, so check before you fly. Additionally, E911 address information should be updated so you can reach emergency services.