It might be possible to directly work with the compressed data, but I'd imagine it would never be worth it considering how quick it is to decode DXT formats. You can always just decode one 4x4 block at a time if you don't want to decompress the whole thing at once.

Either way you wouldn't want to generate mips from the compressed data, because information has already been lost from the source image. Its better generate the mips from the source data (preferably with high-precision 16-bit data) and then compress the mips after the fact.