Concur is simply a database overlay which can be used to assure compliance with travel policies at the booking and reimbursement stages or used for just one purpose or the other.
How long it takes to reimburse is 100% within the control of your organization. As soon as you submit your report, whoever approves it could do so, send it to someone with a finance function and that person could run down to your office with an envelope full of cash.
So, it call comes down to your organization's approval process, how important the people in that process consider your reimbursement and how long it takes for the finance side of the house to process and how reimbursements are actually made.
It's no different than booking. People who complain that Concur won't let them book F are wrong. It is their employer who has programmed the software not to permit F.