The answer is "maybe".
I've had to rent multiple cars simultaneously on my corporate contract twice before. Both times were for rentals picked up at different locations (one airport/ one local) but with cars out simultaneously. The first occasion was a local pickup (National) first and then another pickup at the airport. No problems, and earned credits for both rentals. The second example, however, I was denied pickup at a local office (National at a combined Alamo/National/Enterprise branch) when I already had an airport rental out. Thankfully had another co-worker with me, and had no problem with putting him on that rental agreement.