Survive, yes, thrive, probably not without help. Dry out in mere hours, definitely. If your planter is in full sun (I assume since you are planting sun lovers), I think it will dry out too fast especially once the plants reach mature size. 12" deep sounds better and 18-24" would be what I would aim for.

Don't get me wrong, you can do it with 6" depth, but once july and august come rolling around I forsee the need to water 3-4x per day.

Pro mix is great stuff but it tends to dry out quickly. The container version has that new jello stuff, but I still would be vigilant on the water issue.

I'm thinking some nice annuals packed in there for some dappled shade . . .

Those sun lovers, rudbeckia and gaillardia would be beautiful in full sun beds! Love that platy (mine does better in part shade)! Just my opinion.

I don't think they would survive. If 6 inches is all you have available, I would rip out what you have and start over. Try some alpine type stuff, hens and chickens, that sort of thing. They don't have a deep root system and will be able to take the dry a little better.

Assuming they're pretty small plants, they should be ok this year. You've got 1 sq. ft. of soil per plant. You could extend the time between waterings by inserting a few chunks of clay from the ground in between the plants. A thin layer of a finely shredded mulch would help a lot, too. You didn't say if you intended to keep growing the plants on in this container. I wouldn't try overwintering in a container that shallow without some protective measures... but you probably don't want to bury your decorative planter. Would you be able to put them in the ground this fall and put new babies in your planter next spring?

That said, I have just one more word: Sedum!