Lina started having the option to have water from our water bottles around 7 months when she insisted on having her turn with them.
She really knows the difference between them and nursing and other food. I don't think there's a huge worry about an older baby filling up too much if you nurse on demand.
Seriously, she'll be nursing away, then stop and ask for a "cup", have a drink of water, go back to nursing, stop and walk me to the fridge and get some cheese, have a few bites, hand the remainder to me, and go back to nursing. (When she was 7 months old, she'd just stop nursing and fuss at me until I figured out what she wanted.)
Although, she only drinks from regular cups, straws, and our Camelbaks with bite-valves, so I don't know if sippies would be different. She can't manage sippies at all.