In my tests it's always made quite a difference if your fingers are already on the keyboard, and you want to invoke some specific, non-interactive function; you can usually hit the shortcut, whatever it is, in less than the time it takes to move to the mouse alone.
Few would argue that moving from keyboard to mouse and back between every keypress would be more efficient than just typing one key after the other, as is more usual. The same applies, when activating a shortcut: for example, starting with my hands on the home row, I can do 10 activations of copy (Cmd+C), returning my hands to the home row between each activation, in about 8 seconds. Using the mouse in a similar manner to select the corresponding menu item takes about 22 seconds. Just moving my hand from the home row to the mouse and back again ten times takes around 9 seconds.
(These times are all slightly approximate, because I'm going by eye, because with 2 hands on the home row I don't have a hand left to operate the stopwatch.)
The longer the shortcut, the more time it takes to activate, of course; here, I picked a nice easy one, in the form of Cmd+C. Maybe that's cheating. Some of the fiddlier emacs shortcuts can be quite time-consuming to enter - the rect ones are particularly bad - C-x r C-w, that sort of thing. I wonder how much quicker those are? But I'd imagine they'll still win out over moving from keyboard to mouse to menu bar and back, since for shortcuts you invoke often, muscle memory takes over and you can rattle them off without even thinking.
Maybe all those piano lessons helped after all.
The reader is invited to use their preconceived opinions about microoptimization to decide which conclusion to draw.
(I have no particular opinion about what to do if your hand is on the mouse to start with. Generally I move it back to the keyboard if I don't know how to do something with the mouse, or leave it there if I do. For things such as moving the cursor, or scrolling, the mouse is very effective anyway; usually effective enough that in many cases it's worth using in preference to the keyboard, if you don't have some non-interactive higher-level motion that you could conceivable invoke, such as M-x forward-sexp, or whatever.)