I can back up there isnt an air gap, I've pulled a few apart and not seen an air gap.
The idle current is a concern there are safety issues as mentioned with the welder burning up if left idle, the way round this is to fit thermal trips on the transformers so they cut out when hot.
I reccomend 6013 rods, known in welding circles as the farmers rod, I think a 7014 is a modern version of a 7018 which is a professionals rod, the 7014 being suitable for ac and less sensitive to moisture, check that up first its been a while since I delved into all that, the 7014 will give a better weld, the 6013 a little more forgiving.
Commercial 2kw microwaves make good donors, I had one transformer that would burn 3.2mm 6011 rods which are very aggressive.
Incidently the rod numbers, the first 2 are the strength I think in psi, the 3rd is the welding position 1=all positions and the last refers to the type of weld current ac/dc and a few other things, do a google.