This might seem like a stupid question, but I wonder if this skill works with burst fire mode.
One could argue it doesn’t, because for each click, there’s more than one bullet fired, but one could also assume that it does, because you can’t hold down the trigger and have to press it for each attack.
Is it known how it really works ?
I’'d say: No.
You can fire single shots even when in full-auto mode (if you’re good at it). However, that doesn’t mean Make 'em Count also applies then.
On the flip side, you can fire certain semi-auto weapons in full-auto (if you click like crazy 
) and should the Make 'em Count skill apply?
My best guess, that skill is applied according to the fire mode your weapon is in, not how fast/slow you fire.