According to an article on Bankrate.com from 2011, yes, it can hurt your credit:
With individual liability accounts, the employee holds all responsibility for the charges, even if the company pays the issuer directly. Joint liability means the company and employee share the responsibility for payments, says Mahendra Gupta, author of the RPMG survey.
In both cases, if the card isn't paid and the account becomes delinquent, it will pop up on the employee's credit report and dent his or her credit score, says Barry Paperno, consumer affairs manager at myFICO.com.
It doesn't matter if the company was supposed to make the payment; the repercussions fall on the employee.
"It will impact your score no differently than if you were late on one of your own accounts," Paperno says.
Usually, with corporate credit cards, the employee is liable along with the employer for charges on the card. The intent is to provide the employee with an incentive not to misuse the card. However, this can be a problem if your company is late in paying bills.
In the distant past, I had a corporate credit card. I was not supposed to have to pay the bill, but I did receive a bill in the mail every month. And occasionally, the payment was late. In my case, these late payments never showed up on my credit report. I can't remember now whether or not this card was reported on my credit report at all. And I remember being told when I got the card that I was jointly responsible for the card with the company.
However, your experience may be different. Do the on-time payments show up on your credit report? If so, that may be an indication that a late payment might appear.