The vacuum pipe I assume on yours is the one that runs from the distributer to the intake manifold. It is actually connected to a diapragm (vacuum unit), which in turn is connected to the base plate inside the distributer. What it does is advances/ retards the ignition timing depending on engine load - this is normally represented by the vacuum in the the manifold.
Under heavy engine load the timing needs to adjust, though I can't remember which way it goes ( I think it advances). The same applies to light throttle openings where the opposite will happen.
With a split pipe the vacuum advance unit is inoperative, therefore it won't adjust the timing as it it should. Normally it would cause poor tickover and stalling, but that might only be on the carburetor Unos that I am familiar with. Not sure about the SPI versions.
The ignition timing on a Uno is set at a low tickover speed (approx. 800rpm), with the pipe disconnected/ blocked at the distributer end. The engine doesn't like to run like this, but as soon as the pipe is reconnected it should run nice and smoothly.
What sometimes happens with a failed vacuum diaphragm/ split pipe is that people will adjust the ignition timing until the engine runs smoothly. Problem is, the timing will be out as a result! Might be an idea to check the ignition timing at the same time?
A new pipe can be bought from any motor accessory shop for literally pennies. Cut it to size, and replace your split pipe and you shouldn't have any problems. While you change the pipe, you might as well check the vacuum advance unit at the same time. With the pipe connected to the diaphragm, blow or suck at the other end. If you can feel resitance (a vacuum) then the unit is fine. If there is no resistance then the unit has failed and needs to be replaced.
Best of luck!
Chas