I believe that 'Contorta' is typically grafted, which means that the suckers are probably from the rootstock. Not sure if it's the case here, but many times the rootstock plant is more vigorous than the plant grafted on top and will take over if you let it grow, so I'd prune it out. I'm not sure what they typically use for rootstock so no idea if it's worth trying to root the suckers or not.
My folks have an old plant that has always produced suckers from the rootstock, intermediary and above the graft. Some of the intermediary suckers are easier to use in arrangements as they are somewhat contorted.
It is usually grafted on normal Hazel roots, so you'll get a larger, erect-growing shrub. Most people prefer to remove these sprouts, though you do also get the benefit of a better chance of a nut crop from them.
I assumed that the suckers are more readilly takes root compared to that of the cultivar itself. That said, when I was new to gardening; roughly dozen years ago. I took many cuttings from 'Contorta' itself. Of the dozen I tried one survived. Now I'm delighted my cutting is a medium 'tree' that adorns my current garden. The old one that I planted nearly 30 years past was cut off when I sold the old house. That pained me so badly when they rid off the beautiful specimen tree..
Also, if the rootstock produces nut crop. Yah! I myself would like that very much. That will benefit wildlife in the garden. Good luck with your Hazel rooting. May I suggest air-layering instead of cutting? With ai-layering, you may succeed more readily, I believe.