Yes. Everything that runs over the internet runs over the travel eSIM, exactly as it does on wifi.
iMessage and WhatsApp are tied to your own number, not to the travel line, so they keep working as long as that number is still registered on your phone.
SMS is the exception. The travel eSIM has no number, so a text message that has to arrive as an SMS needs your own line switched on — worth remembering for bank codes.