Yes! Jump Desktop 7.1+ for iOS has the ability to connect to a physical mouse on a stock iOS device. There are some limitations though - currently not all bluetooth mice are supported. Jump Desktop currently supports the following Mice:
To start using the mouse with Jump Desktop make sure the mouse is paired to your iPad/iPhone by opening up the Settings -> Bluetooth. Then open up Jump and connect to your computer. Jump should automatically start working with your mouse.
To configure mouse options (sensitivity, swapping the left and right buttons), open up Jump and then then tap the settings icon on the top left and then Mouse & Gestures -> Physical Mouse . Alternatively you can also change these options while you're connected to the remote computer by tapping the tool icon on at the top and then tapping the Physical Mouse row.