The $49 Aeon doorbell has two pieces, a pushbutton and a chime mechanism that can play many different sounds including custom MP3s. When you’re using SmartThings, the pushbutton is optional: you can trigger the sounds off of any event that smartthings can recognize.
So many people in this community use that. You can set it up so that a different sound plays for a different sensor or at a different time of day. It comes with some built-in sounds, including the chime.
Set up is tricky, so it gets a lot of low reviews on Amazon from people who couldn’t figure out how to make it work. But if you use the custom created device type for smartthings and get help from the community here, most people find they can be very successful with it. 
https://www.amazon.com/Aeon-Labs-ZW056-z-wave-doorbell/dp/B0182XG27Q
Another option is one of the many speakers with sound capability that can be controlled through SmartThings. Sonos is an obvious example, but there are also many others. This is another popular option.
So, yes, you can definitely have a chime sound triggered by many other events.