If Tailscale is installed on your router, then any client will also be able to connect to Tailscale networks.

Fo example, if you have a default route back to your home network on the router, any client will also connect through that tunnel back through your home. This assumes you are using your travel router to connect your laptop as opposed to say the hotel wifi. (In this scenario, your travel router is connected to both the hotel wifi as an uplink and Tailscale.)