Hi Rachael,
Yep... they certainly can. Gab usually sleeps more when she's sick. The last lot of gastro she had she was asleep more than awake.
Mind you, she's teething atm and won't sleep for the life of me, hehehe. So they do vary.
Milo will be ok... just keep an eye on him and get as much fluid into him as you can while he's awake.