Lots of people say they have done this, but I have only done it with limited success despite quite high summer temperatures. The most difficult thing is to get the root going in the first place, and for that you DO need high temperatures and ideally bottom heat. Also make sure you have bought a nice fresh piece of root that has a 'bud' already on it.
Once the bud starts growing away it is quite easy to get the ginger plant under way, especially if it's a good summer and your tunnel is in a good sunny spot. What is less likely is getting the plant to actually grow an increase in the root that you can harvest. Bob Flowerdew claims to have done this but he is in East Anglia and I think he probably heats his polytunnel.
Anyway, worth trying.