You should really ask your corporate travel dept regarding this issue. Some companies are quite good at letting their staff use the corp rates for leisure, and encourage them to do so. However, I do know some companies (especially their compliance dept) which go ape$hit when their corp rates are used for non business travel.

For the hotels, they don't really care and seldom ask for IDs or verification. You are more likely to feel the wrath of your company rather than the hotels giving you a hard time...