Will vines grow DOWN a fence, just like they'd grow UP a trellis?

I want to plant some clematis, and some other flowering vines, on top of the multiple fence posts of my 6’ wooden fence, in pots on little platforms on top of the fence posts. But friends have expressed worry that the vines might not grow well, since they normally like to climb UP things.. but wouldn’t they also climb along the fence, and even down along the fence posts?