Magic Mouse 1 and Bluetooth 4.0
Yes, the Magic Mouse 1 works with standard Bluetooth 4.0.

Bluetooth is generally backwards compatible so that older devices keep working with new Bluetooth hosts (either built-in to computers or in dongle form), although newer devices generally are not guaranteed to work with older Bluetooth hosts.

The Magic Mouse 1 requires your Mac to be running at least Mac OS X 10.5.81, which you would already be running if your mouse is working before adding the dongle. Any 2011 Mac is capable of running 10.5.8 or later, so you will face no problems there.