Yes, in ciV, it's detrimental to rex without surplus happiness... or projected happiness...
if you're rexing next to luxuries you don't already have, or if potentially you're about to make a city state ally with a luxury you don't have, then you can rex 2 cities. If you choose certain policy tracks like piety, it makes it easier, too.
All in all, though, it's very difficult to have more than 6 cities by 500AD, for example. If you do, you need to keep population to a bare minimum and all you've created is a weak, spread out target for the ai. I keep saying 5 by 500AD because every game I play, no matter difficulty, it's all I seem to be able to manage with healthy production and income.
1400AD is around 8 cities usually, with capital and 2 others being 12-14 pop. One or two might be puppets.
Then you have a "foundation". On standard speed you're building happiness buildings in 10-14 turns, making city state allies and fleshing out better policy tracks.