Short answer - yes.
Longer answer: yes, they will either use the chain to climb up or will fall over the edge (but they may not flower as profusely as a proper trailing nasturtium)

I've used dwarf nasturtiums before as they give a good display without going mad. The 'normal' ones tend to grow 20/30ft for me, too much for a basket.

Good idea to use dwarf variety but beware they are a magnet for blackfly!