Yes, suckers are easiest way to start trumpet vine, IMO. Like RG, I have some large Trumpet vines in my yard, and I let the seed pods dry on the plant every year. It seems that the only new plants I get are from suckers, though, because they're always attached to one of my big plants by a stolon. The seeds certainly must disperse naturally, but they don't seem to germinate all that easily ... not where I live, anyway.
I find about 3 or 4 new suckers every year, and if I want to keep them, I just dig them up with a reasonably-sized root ball and replant them where I want them to grow. I dig them when they're between 6" to 1 foot in height, because they're easy for me to handle at that size. That's how I got my first Trumpet vine ... a friend dug up a couple of suckers from his yard and gave them to me. One died, but the other flourished, and I've started 2 new plants from suckers from it.