Absolutely. All Signal calling and messaging is done over the internet. As long as you are connected to the internet without any restrictions, then everything will work just as it did when you were home with your old SIM card.
Your contacts can still reach you at your Signal registered number. Find your Signal number by going to Signal Settings 
and test if your account is active by sending a message to yourself in the Note to Self contact and ensuring you do not see a banner saying your device is no longer registered.
However, in order to reinstall or re-register Signal, you need access to SMS or calls to your SIM card. Contact your mobile provider before you head abroad to make sure you can receive SMS or calls to that number if you plan on reinstalling Signal or wiping your phone while away from home.
