I actually did this when I moved to Raleigh a few years ago. It was much cheaper to stay at the hotel the 4 days a week I needed (since I travelled 3 days during the week) for the first 4 months of my move. As far as mail - luckily I had a friend at home who I had all of my mail forwarded to and she would send me a package each week at the hotel

After 4 months I moved to an apartment. I felt like Eloise at the Plaza when I was staying there