Q:

Do enemies respawn indefinitely in target escort missions?

Enemies spawn seemingly every round on target escort missions. Can I hang back and take care of them completely before proceeding, or will I end up fighting until they eventually overpower my troops?

A:

There are a finite number of enemies.
The Target Extraction missions always end with the objective, "eliminate any remaining hostiles," unless you've already killed them all. 
You can also move your squad into the extraction zone after the VIP and end the mission that way. However, you won't get your loot and any XCOM personnel outside the zone when you end the mission are lost.
XCOM wiki

