Yes it does work like that in multi player lol

and it works well if you have your team in on it.
I suggest the following:
1) Aim at the ground like most "rocket" based games. This spreads the damage to a group of people unlike hitting them directly and making them a meat shield for everyone.
2) Have a backup weapon, like a Bullpup, to shoot up close things. The grenades don't arm themselves until a certain distance, and the force of the shot is enough to kill most specimen, but none the less it is slow - get a backup.
3) Conserve ammo. The weapons are expensive until you level a bit, so conserve the ammo you can and save up for the next best gun.
4) Leave a pipe bomb somewhere behind you for when you forget to look in that direction and things gang up on you. Don't put it too close lol.
5) I've found that if a team (of any classes) buys a pipe bomb each and puts it under someone else, if that person gets a little over their head it will blow up and kill everything, but not them. It comes in handy when camping a hallway.
6) Don't spawn as a Demoman. It has no bonuses for the first wave. Choose medic for speed or sharpshooter for the 9mm damage. Demo can not help in any way the first wave (unless you are already level 5 and spawn with the weapon

)
7) Level this like crazy because you are right, it does level really fast, and it is very strong. I predict a nurf like the medic had because it is definitely overpowered right now and I love it
EDIT ADDING MORE
8) Apparently the pipe bombs don't hurt doors! Thanks Moosecat!
9) Play with a commando. My friend and I just play through normal by ourselves to level my demo, and since he can see health bars, he sees right through my smoke. It is the perfect combo!
10) Playing with a support is nice as well because they are close range with shotguns and you need to be long range if you don't want to kill yourself
11) Although this is given - I'll put it in here because everyone seems to say it. Don't kill yourself. Don't shoot close things or straight down. A stalker at just the right range will really hurt your armor, once again why playing with a commando is nice.
12) Level 5 gets a pipe bomb, woooo yeaaahhhhh... Level 6 gets the M79 and 2 pipe bombs. Better but still... I guess this is TW's way of saying its too cheap to let you spawn with your super weapon.