Oh yes, chillis will grow well in a tunnel. How much light does yours let through? Is it restricted? Because chillis do love hot sun
I was surprised how well chillis have grown directly in the ground in my tunnel (until some newly hatched chicks ate most of the lovely red fruits!) Now I grow them in pots and don't have any hatchings going on.
Anke is correct though that unless you live somewhere really nice and warm, you would be better buying in plants this year to harden off and plant out in a week or so, or you'll end up with nice big plants but no ripened fruit. Perhaps do that so you learn about growing them in this first year, then start off your chillis from seed early next year and fill the tunnel with every type you can find. They are such fun to grow (somewhere on here I posted a recipe for '100 chilli chutney' if you get a good crop. Use the hottest you can grow)
Chillis need similar soil and conditions to tomatoes, but not quite so much water. In particular they hate the soil being cold.