I've worked in a couple different hotels, so I wanted to mention some possible problems you might encounter in this situation. As Enigma01au states, checking in but not staying for a 1-night stay is not a problem. But, trying to get a 4-night stay credit will likely be difficult.

People leaving hotels early without informing the Front Desk by checking out is common (especially for hotels that cater to the business travel market). Housekeeping will usually alert the Front Desk if they don't see any personal belongings in the room. Although the hotel may try to contact the guest, they probably will just check out the guest. Hotels do this because a checked-in but unoccupied room generally leads to a disputed charge.

I can think of two ways to make this work:

1) Talk to the Front Desk Manager and tell him/her what you are doing. Most of the time, the hotel won't care. I'd even go as far as telling the Manager to put you in the worst room so you affecting other guests. The only potential issue is if the hotel is sold old. In a sold-out situation, the hotel would prefer a live person over you, since that live person might generate other revenue (like room service).

2) Check in, go to the room and put the Do Not Disturb sign out. Just doing that might work at some hotels. But, in my first hotel, we had an Executive Housekeeper that tracked everything. After a room had a Do Not Disturb on for more than a day, she would send security to check the room to ensure the guest hadn't had a medical emergency. If you don't want use option 1 above, you can put the Do Not Disturb on and call the Housekeeping Department to let them know you won't need service during your stay. Then, call the hotel on your check-out date and tell them you left but forgot to take down the Do Not Disturb sign. (Technically, that last part is optional...but, it does make things easier on the Front Desk.)

My post might be excessive, based on your simple question. Still, I figured understanding the hotel perspective might be helpful. If you need to earn stay credits before the end of the year, avoiding any potential problems might be good since there are only 3 weeks left before 2012.