It's probably best to assume that if you haven't paid for a seat for the baby, there won't be an empty seat for you to put the car seat in. At least, not an empty seat by yours. I don't think many people in E- pay on-board for E+, so if the seats near you show as full on-line, then they'll almost certainly still be full when the plane takes off.

If you bring the car seat on with you, you can always try to find two seats that are free together after everyone boards, or ask some people to move around. No one is going to volunteer to sit next to a toddler on a redeye international flight, so that should not be considered Plan A.

If you absolutely want the baby in the car seat, you'll have to buy another seat. If not, expect to carry him/her the whole way, and be happy if there are some open seats in E- you can use for free.