I'm going to say yes, but there are severe restrictions. Ipods are designed to work with internet so wifi without internet will have unpredictable results.
There may be a few things that the ipods can do over a local network (without internet). They may be able to backup/sync to a computer. There may be some apps that can stream media or communicate over a local network. Pretty much everything else, however, such as installing apps and downloading media, will require working internet.