Going to have to concur with the other posters here about reading your travel policy carefully, speaking to your supervisor, travel, or finance manager. In a smaller firm you may be able to sweet-talk it, but any external audit would definitely raise a flag on it unless you used Jerry's nifty idea, and even then you should clear it first.

As a further example, I had some instances last year where a points stay I'd booked expecting to be on holiday turned into a work trip. My employer considered it a personal stay and it wasn't reimbursable, and my tax advisor later told me that I couldn't count it as a deduction for business travel expenses either, as it technically wasn't a "monetary" expense.