The question depends on what the mouse does. Here is the "normal" .MouseDown event...
Office VBA reference topic
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You can tell which of three clicks was used - right, middle, and left. You can tell where the mouse was on your screen when it was clicked (using the X and Y values). You can tell which - if any - of the shifts were used... CTRL, SHIFT, ALT.
If the mouse does anything else, the question is whether that something else is normally visible to Access. You would have to check the documentation for the mouse to see whether that programmable action triggers a testable windows event, and if so, which one. If, for example, it triggers keystrokes, then the question would be whether - or how - the keystrokes show up.
We won't be able to answer the question until you can tell us what the mouse will send when using those programmable features. In theory, anything is possible if you can program it and see that it has been used. But as we say in western culture, "the devil is in the details."