No. A join just registers a device with the network, not with a specific gateway. Once joined, it just transmits, regardless if it’s still close to the gateway(s) that were involved in registering with the network, and regardless if those gateway(s) are still operational. It might not even notice that transmissions are not received; it just transmits and hopes that one or more gateways will forward its data to TTN.
Using things like ADR or confirmed uplinks might make it detect that too many transmissions have not been received. But even when that happens, it does not need to join again. Instead, the LoRaWAN stack on the device would then (eventually) lower its SF or increase its transmission power.
See https://www.thethingsnetwork.org/docs/lorawan/ and https://www.thethingsnetwork.org/forum/t/how-often-should-a-node-do-an-otaa-join-and-is-otaa-better-than-abp/11192