Yes, that will work, but a repeater is a very poor and technically inadequate solution for improving your own WLAN. For better WLAN, a WiFi mesh system should be used, one of the cheapest and most technically mature examples of this would be the Xiaomi AX3000 Mesh Set System, it consists of 2 identical routers that can provide a very stable and far-reaching WLAN, including support for over 250 devices and also for the latest WLAN WiFi 6.

The set is a little more expensive than a repeater, but you get a very future-proof WLAN, where the WLAN devices can move freely in the WLAN area without interruption.

Xiaomi AX3000