Will the Xiaomi smart button work?

Yes, all of the Xiaomi/Aqara zigbee devices will pair and work with SmartThings, but there are a few caveats. They do not work well with most zigbee repeaters, and will constantly fall off your network if they connect through an incompatible repeater. Some of the Xiaomi devices can also be difficult to pair initially.

I have lots of Xiaomi and Aqara devices working with SmartThings and really like them. They’re well made, tiny, look nice, and can be found at really great prices.
Ikea Tradfri devices work great as repeaters for them.

If you search the forums here you’ll find lots more info, but the best place to start would likely be here:
https://community.smartthings.com/t/original-aqara-xiaomi-zigbee-sensors-contact-temp-motion-button-outlet-leak-etc/113253