Can staying in a bath tube with hot water make you sick if you're in there to long?

I wouldn't think it will make you sick however you will start to have a shriveled look from water leaving your body cells due to osmosis which basically is the movement of water from a place with no sugars/solutes to a place that does have them eg the bath. Which is why people should always have a drink of water after a long bath to stop themslfs becoming dehydrated.

Also if you stay in there an exceptionally long time it may have some bad effects on your body cells as they will have all shrivled up.