How important is the 12V battery vent tube? My 57-reg Prius doesn’t have one. There’s just a hole in the floor where it should be…
You'll never notice it to be honest about it unless you are able to get some really cheap old style batteries which may be the case in your country I don't know I have a few cars with the tube is long gone and they all have batteries in them and work everyday nobody's ever smelled a thing lol You got to realize that battery fan blower pieces tubing square that goes across the battery has a cutout in it that blows hot air right on top of the battery about where that tube is so anything coming out of that tube or out of that hole where the 12 volt is is being whisked away when the HD fan is on blowing everything out that vent in the rear quarter right to the side of the battery so not likely you're ever going to smell anything with the quarter panel covering there the vent tube and the fan working just not a likely event.
it depends on your view of personal safety. in the unlikely event that would cause the battery to emit poisonous/explosive gases, the tube directs them outside the car, instead of into the passenger cabin
Could that tube have disappeared under the door through the hole, or would one have to physically remove it?
you would have to physically remove it. there is a plastic elbow that snaps into the port on the battery, and the tube fits over the elbow. some people replace their oem battery with one that doesn't have a vent port, and toss the tube and elbow