Yes.. any universal repeater should work... ie that is what universal means.
For most people another Apple router is far superior solution.. since apple built in a proprietary WDS system that is easy to manage and maintain.
All repeater systems have issues.. but universal type will be much less reliable.
For example the IP addresses of all clients behind the repeater are masked by the repeater itself. As far as Airport is concerned all traffic is from the repeater. Nothing will appear then in your airport utility to show clients on the network.. and no controls are therefore possible.
Repeaters tend to be hard to manage.. they disappear into the network and it might be difficult to locate it after a few IP changes.
Repeaters slow the network connections by at least half. And increase latency often by much more than double..
Some modern mesh systems get around these limitations but it must connect to the main router whichever device that is.. and all mesh systems consist of the same units from the same manufacturer as it is proprietary system just as Apple system is unique and cannot be used by another brand.
So they can work.. in some cases work well.. I have used a number of repeaters including Apple to Apple ones..
In the end I recommend against using them for anything except data.. and only in situations where ethernet is truly impossible.
