Would there be any interesting 2o structures in the proteins from any new amino acids (etc. etc.)
All of which is to say something of a sensitivity analysis on the system as it exists, is the optimal or near optimal for forming animal/human proteins, compared to other, umm, ingredients (assuming the same general form DNA--> tRNA --> amino acid --> protein)?
...and would the current proteins which unzip and stabilize DNA (and correct mistranscriptions) work as well on the DNA with 8 base pairs?
The interactions of proteins with nucleic acids are varied and complex. If the alternate bases were bound to phosphorylated ribose or dideoxyribose, no doubt some of the proteins would interact without a problem. But I think there would have to be a huge effort to make a system where these new bases could be used to code for proteins or functional RNAs. To make functional novel biomolecules is not currently possible, I think, since we still have such a long way to go to tie structure to function to the point that we could design new functional molecules de novo.
I do see some potential here, for example to create functional bacteria that can only grow using the artificial bases, which do not have the ability to synthesize those bases. They could be used to produce drugs or break down toxins, with far less concern that they could escape into the environment.