My understanding is that yes, you can. The people we were looking at building our permanent fence also offered temp fencing.
Only trick is you need to get on to it quick smart because once your site supervisor puts temp fencing up, they won't reimburse you if you later go & erect a permanent fence or replace the temp fencing (& yes, you can build permanent fencing once the temp fencing is up - you just need to organise it with your site supervisor).
We've found this out the hard way because we organised to put permanent fencing up but PD's wires got crossed & the site supervisior never knew about it...by the time the fencing company were ready to go, PD were about to lay the base & they'd already put temp fencing up (instead of waiting until after they'd laid the base, like most companies) &, whilst we can come & put fencing up if we want to, they won't reimburse the cost of the temp fencing. As it is, we've decided not to put it up yet - the last thing I want is damage to my nice new fance.