potenially idle problems, yes.
you'll get idle problems if your mixures are shot - usually down to air leaks. if you block the end off is your idle any better? (bear in mind the mixture may have been altered to pass emissions and compensate for the leak)
I can't tell you exactly where this pipe goes, but the MPG meter works on the intake vacuum.
From my previous dealings with pierburgs they are a nightmare with vac pipes and valves everywhere so lots to go wrong. They also don't have reliability over 8 years / 100k miles so if you can do a weber conversion (direct replacement or twin 40's if you are hardcore!).
Hope this is of some help, my experiences are with VW pierburgs not BMW. Can you give a model code for the carb (probably 2E2 or 2E3)?