That depends, I run in new balanace's minimus trial on pavement.
It takes a long time to build up the technique for running in them landing more towards the front of your foot than the heel. As well it takes longer to build up the muscle and ligaments.
First time I ran in my Vibrams (before I switched to minimus) I ran 400m and my calfs hurts hurt for 4 days. It needs to be a slow transition, that will allow your body to adapt. If you just go out and run and overdo it things are not going to go well.
I can run upwards of 5km+ without issues now, but I do not run that far very often, maybe 4-6 times last year.
Look up the pose method of running, look at the drills and talk to your CF trainer about it they should be able to help you there or at least point you in the right track. Lots of videos out there on it and how to learn it.
Go for about 100m run, see how you feel the next day slowly build up your ability to increase the distance until you are doing WOD's.
Running on the front of your foot is a softer landing than heel striking so learning to run that way on pavement will be better than running with softer shoes and heel striking.