Will Missing Teeth Help Braces Work Faster?

unfortunately, probably not as missing teeth on just one side makes keeping the dental midlines centered on your facial midline much more difficult (usually anyway!

The answer to  your question is: it depends!  Often missing one tooth in the back can complicate treatment.  Missing an upper front tooth may also make treatment with braces take longer if you've had a lot of tooth drifting.  TOn the other hand there are cases where missing one tooth in the lower front could actually speed up treatment.  Orthodontics can be a bit complicated and often the best solution to a patient's problem is a unique treatment plan designed just for them, taking into account the unique attributes of their case. 

Sort answer: not likely but maybe

Long answer: If you were otherwise crowded, yes it can speed it up. If you had a tooth pulled for other reasons it can actually lengthen treatment. If you had the teeth removed years ago and they have drifted in unhealthy ways, it can also effect the length of treatment more than if  they were recently pulled.

Your best bet is a consultations. Most orthodontists will do them free of charge.