Oh yea she'll bring pokémon up until the ranch reaches level 20.
She chooses a pokémon from random (I think from her trade list). It's when you exit the game she gives a hint as to which one. I personally haven't seen her bring a charmander. You have to wait a day for her to bring them. It's usually 3- 7 pokémon in a day, so she would stop bringing them in roughly half a year. If you haven't deposited any.
http://serebii.net/ranch/ranch.shtml
So she will stop bringing when there are 500 pokémon
Also you don't have to trade, you have an option saying yes/no.
You can only trade if you deposit a pokémon she says she wants to see anyway. Dx