There is such a thing as root-bound but no a plant will not strangle itself to death. What it will do is suck the moisture and nutes out of what little amount of soil there is in relation to the amount of root mass and can dry out and or lack needed nutrients easily because there is not enough soil to hold enough of both for much time at all. It also stresses your plants and reduces growth and yield and quality.
Once a plants roots begin to circle a pot the plant is then under a degree of stress and the worse it gets the more the stress increases. A plants root mass will pretty much equal its above soil growth/size so you need enough pot size for roots to grow and spread out and you need enough soil to hold moisture and nutes so the roots can drink and feed.
Whenever you pick a pot size try to think like a woman who is looking for a guy for sex and remember that bigger is better.
You can never grow in to large of a pot (unless you have area/size/height restrictions of course) but you can very easily, and most people do, grow in pots that are to small.