It depends. I've ridden on, say, the Thanet Way (A299) that has big hard shoulders, is flat with good sight lines and wasn't terribly busy at the time. While it was not much fun, and I only did it because I was in a hurry trying to catch up with someone else, I didn't feel in danger.
On the other hand I recently mis-navigated myself onto the A249 just North of Detling. A smaller dual carriageway. I only needed a couple of km (if that) until I could get off it again but it was horrific. Quite narrow, poor sight lines and incredibly busy. I thought better of it, turned round back up the hill that I'd just come down and found another way.
I regularly drive up the A1 in the Peterborough-Newark sort of area. I really wouldn't want to ride a bike on there. I don't much like driving a car along it.
I drive down the A299/Thanet Way, at 70mph, on a regular basis, I'd be very surprised to see a cyclist there, and whilst I'd move into the 2nd lane to pass, many would not.
Given that there is a perfectly good cycle path beside it (I've ridden it twice), personally I cant think of a reason why you want to be on that road, even if it is better than most.
I been driving up and down the A2 for over 40 years, I remember that up until the late 1990's it was regularly used for time trials.
Whilst it may still be perfectly legal to do so, given the volume and speed of the traffic on what is to all intents and purposes a normal three lane motorway, you would be mad to cycle down the A2 today