Generally, the answer to your question is no, the hospital will not allow a family member to stay overnight in the same room as a patients. However, the hospital will make allowances by letting you stay by your wifes side for as long as their visitors hours allow. Not all that long ago my father took gravely ill, and was hospitalized for just over two months at Rochester General Hospital. He came as close to death as anyone could get. In that entire time, from 7:30am to 9:00pm my mother every day stayed by his side. At that time they had been married for 61 years. For me to say it was a difficult ordeal for both of them would be a gross understatement.
But the point here is that for all intensive purposes my father never felt alone, because she was there when he awoke in the morning, and stayed until he went to sleep at night. There were many times in the afternoon hours I would see my mother, while sitting in a chair, napping by my fathers bedside, her head next to his shoulders. By the Grace of God alone this year they will be celebrating their 65th Wedding Anniversary.
May God Bless You Both, and Take Care.