Because ascorbic acid depletes all of the chlorine in the pool (which is why one usually uses PolyQuat 60 algaecide during the process to help avoid algae growth), one should not swim during this process. After the stains have faded and you've added metal sequestrant, then you slowly start adding chlorine. Once you start measuring a chlorine residual getting close to the recommended Free Chlorine (FC) level for your Cyanuric Acid (CYA) level, then the pool is safe to swim in again.
Now "safe" is always relative and it's your own pool so you can always do whatever you want, but when there is no chlorine in the pool, bacteria can grow quickly and depending on what kind of bacteria are growing, this can become a problem if you take in too much that overwhelms your immune system. Though the risk is low, it is far far lower when chlorine is present.