Yes, from your description it COULD be a climber but it could also be a number of other things too. The canes coming off the main canes are called laterals and that's a good thing. The more laterals you have the more blooms you'll get.

It sounds like it is a once blooming rose. That means it only blooms once a year in the spring or summer on last years wood. So if you had to cut it to the ground this spring and all this growth is from this year it would not bloom now until next year as long as all those canes survive winter. Spreading the canes out as horizontally as possible will encourage more laterals and blooms

There is also the chance that what ever rose it was it was grafted and the grafted part died off. That would mean that this is the root stock coming up. Most all of those are once bloomers so you would have to wait until next year when it blooms to try and ID it.