Yes, it absolutely needs the line from the tank to the tuned pipe. However, unlike calvino, I don't think that will solve all your problems.
If you're spitting raw fuel out the exhaust then you are flooding the engine. The carb needles probably need to be reset and the engine tuned.
If you can find out what kind of car it is and post that up maybe we can help more.
Or you can find a hobby shop near you and take it to them for identification and help.

I hope you didn't pay a lot for it. Used nitro rc's are always a gamble and that one looks like it's been wrecked a couple times.