Can you explain what you mean by letting them grow "naturally"? I assume you want to train your TGs to be climbers, so you will have to be vigilant about training them and attaching the canes to the trellis as they grow. Your trellises should work for that. This rose can be trained to be a climber (with training) or a shrub (with pruning) -- either way it needs some attention from the gardener.

As festiva mentioned the training/tying off of them, I will skip that part. Not sure what area you live in, but if you live in a warm climate probably 1 teasing georgia could fill that space as a climber. 2 will definitely fill that space. I'm in zone 5 and even my teasing georgia gets big after complete winter dieback.