In accordance with general telecom industry practices, Twilio provides ongoing voice and SMS service to porting-away numbers for ten days after the scheduled port date. This practice provides for overlapping coverage, thereby minimizing the likelihood of downtime.
After that ten-day period, it is up to your new carrier to provide voice and SMS service because Twilio will no longer have control over the number. Therefore, as long as your new carrier executes the port properly and can provide both voice and SMS service, you should experience no downtime in connection with a port-away request.