Agreed, your employer's policy will trump anything anyone says here, but with that said, as a general rule I'd think that unless there was a requirement to use some form of approved payment method (corporate T&E card, for instance), it should be OK.

A grey area arises if the use of an alternative payment method results in some sort of "kickback" to you - e.g., cards with cash back or points or other benefits accruing based on the spending. But if this is a gift card that just has a particular balance that can be used for payment (like a preloaded debit card) it should be fine.