Is there a way to hop up onto a parallel curb? The scenario: you're riding in a curb-adjacent, paint-only bike lane. You happen to look over your shoulder (or in your mirror) and see a vehicle approaching from behind, either fully in the bike lane, or close enough that they can't safely pass. Assume that veering to the inside of the approaching vehicle's path (away from the curb) is not an option, and that there is no time to slow and dismount onto the sidewalk.

Is there any technique which can be used here to quickly lift the bike both up and to the side, while traveling at speed, such that you could safely continue your ride on the raised sidewalk until the danger has passed?

Answers that do not require suspension would be ideal, and it would be especially helpful (though improbable) to find a technique that can also be used while carrying reasonably-weighted (~10 pounds) panniers on a rear rack.
You're talking about a "bunny hop" and it can be done at speed on a loaded bike but it's high risk. You'd almost certainly be better off jumping off the bike and rolling. US Bike Trials call it a "side hop", but in anglonesia I've mostly heard it called a bunny hop. 

Here's a photo of the 2006 Cycle Messenger World Champion doing more or less that at about 30kph, but wearing a backpack rather than panniers:



Note that at the world championships for people who ride loaded bikes fast all day about 3/4 of the competitors slowed down and used the pram ramp or just stepped up the curb (my photos are of the ones who took the more exciting approach, obviously). In this case they rode along the road, then had to go onto the footpath and turn very slightly onto a path, so slowing down to use the ramp definitely cost them time. 

If you're expecting to do this, IMO you're better off learning to dive roll properly. Either through a martial art like aikido or ninjitsu, or through gymnastics. That skill will help you in a much wider range of situations than "if I have a couple of seconds to get organised I can bunny hop". Also, the most likely result of trying this is that you end up hitting the curb with the bike, then the pavement with your body. So rolling will be useful either way...

For me, it took a slightly disturbing number of crashes in my late youth before I was seriously injured, largely due to my ability to roll (loosely speaking, via martial arts training). And when I did eventually break my humerus it was because a roll failed. Even now, I've been riding everywhere for 30-odd years and still my major injuries have all occurred through both my own stupid fault and in effectively single vehicle accidents. The "hit by car" ones have all involved a bit of flying through the air, a roll then a lot of very politely explaining to the motorist that I would like them to give me their insurance details. Now. THANK YOU.

FWIW, I can do a hop like the one shown, on my commuter bike, with panniers, but only with careful preparation and a 90° approach. Jurgen's flying leap approach is not one that I'd try if there was any way to avoid it.