In my experience, so long as you've got the appropriate ID to show at the desk if asked there's no problems with using discounted codes related to your workplace (even if it's not specifically a work trip). The majority of staff I've encountered don't even ask for ID anyway, but it's always nice to have if just in case.

As also stated by party_boy your company could get better discounts regardless (or it will help them reach their promised targets for number of rooms booked) so they're unlikely to have any issues with using the code either.