A couple questions about bottle feeding and hospital?

I had a couple questions that I want to know. I am due tomorrow and just wanted to clarify a few things. I will be giving my baby formula and not breastfeediing. (Please do not ask it's for medical reasons and I'd rather not discuss it). So when you have your baby at the hospital I know that they will provide formula but from what I have read women breastfeed immediately. Will they give me a bottle of formula right when he is born or do they wait a bit? My hospital does provide formula because I called and asked just to be sure. Another question I had about it was will they still let me room in and everything with my baby even though I am formula feeding? This is really important to me because I want my baby to stay with me and my husband no matter what. I plan on telling the nurses as long as nothing is wrong we don't want him separated for long periods of time. I will be induced on the 12th if he isn't here so I know I can talk to my doctor before if I need to but help is really appreciated.