It would work. We did that with a stretch of 4 nights in DC last summer. However, we did not tell the frontdesk about it as we knew we were skirting the system so to speak. So we actually did the check-in check-out thing every day. We were travelling with 2 backpacks and our car parked at a Muni garage 2 minutes walk from the hotel. Therefore, we just checked out each morning, dumped our backpacks in the car and then took the metro to The Mall. When we returned in the evening we retrieved our packs and checked in again. Yes, we stayed in different room each night. It did not bother us.

For a 2 week stretch though, I think you are pushing it, especially if these are PL stays.