I've shot a pneumatic set of standards once. You could actually hear the "PSSSSHHHHTTTTTTT" noise as the tubes filled with air, just prior to the targets appearing. No advantage there, right?
Hmmm, double plugged I don't think I ever really heard it. Can't remember doing so anyway. Anyway, I can't imagine the hissing noise would be any longer than the beep tone (.30-ish second).
Just ask the RO to hold the timer closer to your head if you're worried about missing the stop beep.
As long as they are running only one person at a time. I don't know what the plan is for Lethbridge, though I assume it's one at a time...? Again, with the pneumatics they usually ran 3 people at a time, and I think one of the reasons they went that way was to avoid the stage being a bottle-neck, as it was 4 strings from 50 (3 targets/6 rounds/6seconds), 25 (3 targets, 6 rounds/reload 6 rounds/6 seconds), and 10 yards (strong hand then weak hand/I forget what the time limit was). So it was a slow stage to run. Anyhow, none of this is meant to be judgmental; only comments from a specific historical perspective.
Also, if your gun is going off at the same instant as the timer you might still not hear it. Not likely, true, but possible. I'm just saying....
Remember, overtime shots are not -10, they're -5 (at most). As long as you're shooting A's, it doesn't matter how many overtime shots you take as the penalty for shooting them, and the value of the hit cancels each other out.