The simple answer is no
It’s extremely rare for a supplier to disconnect a customer’s energy supply.
Disconnection is a last resort, when all other avenues have been exhausted in trying to recover debt from a customer by all reasonable methods (email, phone and letter) over a considerable period of time.
Provided you are not in debt and you have not altered your meter in any unlawful way, then there is no chance that your supply will be cut off during a switch – even if either supplier chooses to block the switch. In the event that your switch is blocked and your current contract ends your current supplier will move you onto a standard tariff until a you are switched.