Will a circuit breaker always cut off if there is overcurrent to it
 

I recently got a bunch of high amp circuit breakers from someone and am planning on selling them, but I am a little worried about the liability. If a circuit breaker works in the sense that it can draw power, is it safe to assume that it would shut off if there is overcurrent to it?

nope:no:

A quick web search on Federal Pacific (FPE) panels will show the potential problem. Here's a video of another old brand of breaker not functioning:
http://www.youtube.com/watch?v=uMV1jmDn3o4

If they are new I woild sell "as is". If used I would not.

The theroy says it should, but the reality is, used breakers should be dumped unelss you have the equipment to test and certify them.

[A sample of] new breakers are tested at the factory for 10,000 tries.
You could test your breakers 100 times and still not be sure they will work on the 101st try.

http://en.wikipedia.org/wiki/Sunrise_problem

BTW, consecutive successes with no failure is "right censored data", so to do the reliability calcs I guess they assume it would have failed on the 10,000 plus 1 try.

But, how often will a house breaker be called upon to trip?
This is the "mission length"; how reliable is a breaker that fails in less than 10,000 attempts when it only needs to work on 1 or 10 or 30 overloads?