Nah, plants will keep bearing so long as you keep picking. What makes them stop is if you miss some fruits. Then they figure they've completed their reproductive cycle.
I have only 2 potted tomatoes, and a potted spaceship squash. Rental house, so I can't put in a real garden.
On the up-side, my tomato plants have little green tomatoes on them already.
I rent as well and treat my garden like my reptiles, don't ask don't tell. But my rent man never comes by.