Does rust beget rust and the removal of rust spots on a bike
 

I've been cleaning up my '86 Trek 400 Elance; I've been going through the sizable paint chips, removing the rust through abrasion, and touching the spots back up. There are a fair number of spots and it is a lot of work. I'm wondering, if I leave the small rust spots alone, does this accelerate future rusting...beyond that that would occur if I simply had the same spot with bare metal instead of rust? In other words, does the presence of rust accelerate future rusting?

Also, I've been looking for a chemical or some other manner to remove the rust that isn't so labor intensive but want to leave the paint intact. I've considered an oxalic acid dip; however, it is winter here and I do not have a well-ventilated area to work in. Is there a non-toxic alternative for a not-so-well-ventilated space?

The main thing that drives rust is the iron reacting with moisture, so rust begets rust in the way that one rust spot(rust is permeable) acts as an access point through which fresh metal can be exposed to the elements.
If you were to take something that has started to rust and put it somewhere perfectly dry you'd basically stop the process dead in its tracks. The ultra-crude version of dealing with rust is oil/grease/wax.
A dab of oil/grease/wax will act as a barrier between the metal and the environment and stopping the process.
The trouble with this approach is that these substances have limited staying powers when compared to paint for instance, so the treatment has to be renewed periodically to remain effective.
Car parts stores usually have something called "rust converters" or similar, it's a chemical that is applied directly on to a rusty surface(I'd remove any loose flaking first though), and react with the rust to seal the metal off from the environment just as a coat of panit would have done.