If the condenser is broken it will do what you described. the condenser basically reduces the size of the spark across the points (they spark when they open and close). If the condenser is broken the spark will be bigger and the car will run ok for a while when the points are still clean/new, but will burn the points over time and after you have done a few km (took about 15km on my car) it will start missing. This gets worse and worse as the points burn more and it starts backfiring etc.
I suggest you take the points out and check the contact faces. If they have marks on them then the new condenser you put in is broken so they got a bit burnt. Clean them up a bit with a points file until there are no marks left and they should be good as new. I used sandpaper on mine, but have been told this is a no-no (don't know why).
Edit: and in answer to the question - Yes. My brother's car recently had all sorts of electrical problems caused by new points and a new condenser. We swapped the condenser out and it fixed all the problems. The new condenser that had been put in was actually a little domed on the end
