It will not! Float conducts a soft credit check that does not impact your credit score. This soft check is used to verify your address and birth date only.
You've likely had multiple soft credit checks done by various other vendors. The most common types it will happen is when you’re pre-approved for a credit card or when you check your own credit score.
Another benefit of using corporate cards, rather than your own personal cards is that if in the unfortunate circumstance the company does go under, you would not need to pay any money out of pocket