Will a dishwasher sterilize bottles for canning?
Absolutely not. You need to boil them if you're even THINKING about canning. Chances are you'd be fine, nice acidic relish to keep the bacteria down...But do you want to take the chance?

Even if you have one of those dishwashers with a nuclear "sterilize baby bottles" cycle, don't trust it. For canning, you need them as close to medically sterile as is possible.