Yes they can. I've had mine run over with the lawnmower. I've dug one up accidentally. I've moved them at the wrong time of year. Just mark the spot and wait. It'll grow roots and then you'll see green coming up in no time.

As long as the crown remained intact, the plant will survive just fine. As shebear pointed out in her examples, clematis,like any plant, want to survive and will often do so after various traumatic events.

Not sure what you meant by the pillar in the pot. Possibly the trellis put in there for the plant to grow up? Unraveling all those stems from a trellis in the pot is difficult. In the future if there is a pillar in the pot and you can't get it off, try cutting most of the vines off the trellis and then removing the root ball with the crown from the pot. Plant the clematis deeper in the ground than it was in its original pot, and keep it watered. Pruning off all those vines will stimulate the plant to send out new vines and you won't have vines that are damaged from trying to unravel them from the trellis in the pot. Might sound dramatic, but the plant won't mind.

I am also curious about the planting mix you put the plant in. Is this a mix for pot grown plants or a soil amendment that is supposed to be mixed into the existing soil in the ground? Sounds like a soil conditioner to me from the description although I have never heard of it before.

Really, the most important thing to remember is to plant deep and allow the roots to develop. A climber or vine needs three years to develop and the first three years should go into root development. Plant deep, keep the bottom mulched and water in. Best to probably prune and forget for this year.

BTW, I often plant young clems in the same hole as my roses, they do fine.