Yes an engine can keep running with a pressure line failure and exactly as you said often it runs poorly. The degree of effect at the loss of a pressure line can run almost from little effect up to complete and immediate stoppage. The variables are many: mixture setting and even fuel tank orientation and tank height/spray bar relationship and even ventruri size.
Some of the earliest Saito's .45's and some .50's had no pressure fittings for tanks and needed none. The loss of muffler or pressure line will almost always result in the loss of head pressure at the carburetor so the effect is normally poor running or worse.
John