It's no worse that any other urban sprawl that you're likely to visit. 'Locals' on the most part tend to keep themselves to themselves, but you do tend to pick up and anti-student vibe at times -- ironic considering that the university is one of the main drivers of the local economy.
Generally, you will see chavs around no matter where you go, such as Lipson, Mutley, Union Street, etc. but if you're enjoying a student night, you tend not to notice them anyway.
If you're that concerned about finding yourself in a spot of bother, just avoid Union Street on Saturday nights, and stick to the "bubble" which the university provides. The only time you really tend to notice the chavs are when you visit places on non-student sponsored nights, or if you decide to stay over summer when all the students inevitably go home.
Use your common sense and you'll be fine.