I would almost bet a surprising number of the cars going thru the park have a firearm in them already.
From the park service web site:
"Weapons
No firearms or weapons, including state-permitted concealed weapons, are allowed in Yellowstone. However, unloaded firearms may be transported in a vehicle when the weapon is cased, broken down, or rendered inoperable, and kept out of sight. Ammunition must be placed in a separate compartment of the vehicle. "
so the guns are there just unloaded, so how longs it take to load up ?
I've read to many stories where they find someone that gets attacked by a bear and had a handgun and never got off a shot, as in most situations it the surprise that gets you. As for poaching I read the other day where they prefer a spotlight and a bow, we saw where a bull elk was killed in RMNP a few years back, shot with a bow and the head removed, within 100 yards of a gas station on the edge of town.
all that said I will probably not carry a gun, I'm just not gonna be worried if some one else is, after all I got my pepper spray