Yes, whether the condenser was installed with a radio or not, you can see what a drastic difference it does make if you ever have a distributor apart... remove the condensers (in dist. and on the coil) and manually open and close the points. With the ignition turned on and in subdued light, you'll see a noticeable spark. Now reconnect the condensers and try again; no spark.
The idea here is that the condensers
do suppress sparks which shorten the life of the contact surface, whether it is the distributor points or a voltage regulator. RF (Radio Frequency) is a byproduct of the spark, thus the noise.
All the condenser is is a capacitor. Anyone with experience in electronics can attest to the fact that these devices are very failure prone as they tend to 'dry up' due to age and exposure to heat... and sometimes they short out. This is why when a radio is restored, ALL of these condensers (or capacitors) have to be replaced. It's cheap insurance.
I could be wrong historically about the installation of condensers from the factory and it probably varied by each vehicle manufacturer. At any rate, installing a condenser in an appropriate location can always be considered an upgrade.
Sometimes at car shows I see vehicles that have undergone a meticulous 100 point restoration, and sometimes on these cars I see the owner has meticulously cleaned and reinstalled the
original condenser 
I've had these things short out and start fires!
Maybe we should start another thread about this and discuss the particulars of the condenser... just so that we don't detract from this help thread and get more input... The general idea though being that if it's an oldie, replace it. That way you'll at least eliminate that as being a problem
and a source of future headache.
The problem could be any number of a thousand things though, Wrenchbender's got you covered on a few tests you can do in the mean time to further narrow it down.
