Morning suziequeue,
we have the food bags and caddys. The bags start to decompose fairly quickly once any wet/damp food is put in. I change my food bags about twice a week depending on how much/little food waste we have. Usually potato peelings and egg shells. If the bag is looking a bit damp I usually double bag as OH hates using them, plus it is easier to get the bag from the kitchen to the bin outside without leaving a trail!! The big food caddy bin is reasonably secure and it doesn't smell, we have ours inside another bin. See above!!!
Anyway, yes the bags will break down in the compost heap but I think they will have started to break down before you are ready to use them. You can always try it and see what happens.
Hope this helps