Yes, keeping the top growth smaller will stimulate the root mass to be smaller very much like bonsai, but it's truly not the best thing to do for a healthy rose that you want to climb.
Climbers typically will grow their root mass first so that it is large enough to support the top growth it will want to put up. That's why you see little top growth on a climber that is planted in the first couple of years ... even when it is planted in the ground. The rose is growing roots and preparing itself for future growth.
Roses renew themselves by putting out new basal canes because old canes become less efficient over time. This is genetically programmed into the plant. People do grow trees and roses in containers, but, in my opinion, large roses in containers never become the roses they were meant to be.
When a rose is grown in a container, keep in mind, that every few years, it is necessary to re-pot the the rose, give it a root prune and replace the soil due to the salt build up in the soil from the fertilizer you have fed it to keep the rose productive and beautiful. It doesn't matter if the rose is a climber, an old garden rose, a miniature rose, a floribunda, a polyantha or any other class of rose.
A rose that does not have want it needs ... not enough light, not enough water, not enough nutrients, etc., often grows into a weak plant that is more disease prone.
'Dublin Bay' is a solid rose, but like any rose, if you cannot give it what it needs to be a successful plant, you will never see the rose at its best. I guess what I am trying to say as diplomatically as possible is that DB may not be the best rose for this kind of siting.
However, I do not think you need to give up your dream. I think you need to go about it a bit differently. There are climbing flowering vines that do grow well in containers that don't mind having their roots in a shady area and will also reach for the sun and will thrive is the situation you are describing. You could plant those in the pots at the base of your pillars and then put a smaller weeping rose in a container and hang it from the top of your porch. Yes, these plants will need re-potting, too, in time, but it's a lot easier to deal with a smaller plant when you are trying to re-pot a plant.
Others on ATP gardening in your zone may be able to give you more specific ideas on how to realize your dream. Dreaming about what we can create is very much a part of gardening.
Smiles,
Lyn
