No, the Conners are working class/blue collar. The whole appeal of the show is that they're the American Every Family (at least in a certain socio-economic bracket). They hold down long-term employment (and if they do find themselves unemployed, it's due to something like outsourcing or downsizing, not because they're unreliable employees or just flat-out don't want to work), are home and car owners, put three meals on the table every day, and are conscientious parents. The humor is in the relatability.
The first example of white trash on American TV that comes to mind for me is the Crowder family on Justified, especially characters like Dewey Crowder. If you're familiar with that show (you should be, it's great)... yeah, there are some low-income surface similarities, but that's a whole different lifestyle than what the Conners live.