I had the same question. I ended up visiting our intranet section (there's also a big bulletin board in our building) that shows you the company discount benefits we have with all kinds of vendors, from car rentals to hotels to Dell computers. If you work for a big company there's definitely a bunch of discounts available to you. (Cell phone plans are probably the #1 category, all big companies have one or often 3 carriers that offer a %-off.) In my case, the codes posted on that bulletin board (which is clearly targeted at personal use) for the rental car companies were the same codes that the travel policy document listed. So I was able to book with confidence knowing everything was above board. The car rental website even asked me if this was traveling on behalf of and I said no, and the confirmation said "travel type: leisure."
This makes sense too, because your company doesn't pay the difference, they just negotiated the rate, sometimes in exchange for exclusivity or just preferred status, for their business travelers. So they don't care if you book 50 personal nights a year on that code. As for the hotel, they hope you'll use it too because it gives you a reason to stay with them instead of booking at a competitor, or even booking them through Priceline/Expedia/Hotwire where they would have to pay a commission. All this increases the ROI of their signing the corporate discount deal even further. So this is why I believe you'll find that 99% of the time, you'll get a yes.
If you don't see the code listed among the other corporate discounts, I'd agree with the others that it can't hurt to ask HR explicitly just to make sure there's a different situation that you don't know about.