My garage door opener switch was run to a 3 gang box and just dangles through the opening in the switch cover plate. Can I use a 15 amp switch to open/close the garage door or do I need some other type toggle switch?
I assume you've traced the wires to the opener itself? You should be able to purchase the correct wall mounted garage door switch to match the brand of opener. Ultimately you need a momentary switch and a doorbell button usually works just fine. The problem is the third wire which is probably a manual light switch from the stock wall mount switch to the opener. Find the model number of the opener and download the manual.
To answer your main question- no, you cant use a standard electrical toggle switch for your garage door opener. (Well, not as intended, anyway. You would probably have to flip the switch off then on to get it to do what a single doorbell button press would do.)
A switch can be used for any voltage from it's rating or less, voltage wise. Thing is, a garage door opener button is momentary, where a wall switch is maintained. There is the possibility of damage if you leave a switch in the on position too long in an application like this. I wouldn't do it.
The problem you have is that someone ran this low-voltage wire in the box with the line voltage wiring. This assumes the wiring is something like thermostat wire or what came with the opener.
I would remove the wiring from that box and mount a regular opener button to the wall.
And @gregmac makes a good point. If this opener is newer, as in maybe ten years or less, then a regular switch may not work, or at least it will not give you all the functions that the opener offers.