On the use of coax as an antenna you run into a few things.
One is only the outer shield is impinged upon by the passing rf wave, so whatever length of coax you have, that's the total antenna aperture, not the inside center conductor PLUS the outer shield.
Another aspect is if you only connect the center conductor to the radio and no antenna elements on that same coax, the only way a signal can get to the center conductor from the outside is via capacitive coupling, and that will be very scant since only the very outer layer of the shield has rf flowing on it, not the inside facing surface of the shield.
It doesn't take much of a conductor to make for a decent vlf/mf/hf antenna, USN did a study and found that with a decent groundplane (ie a US warship plus the entire ocean) you only needed about 6 feet of wire, a coupling device to make the hi to lo z transformation would of course be spliced in between coax and antenna.
Case in point, I had a 1/4w cb antenna on top of some mast up about 10m, with a decent grounding wire run from base to ground stake. That thing was amazing from vlf to hf and on 6m too, of course I had to use a tuner for best results but it was an excellent dx antenna. Not very good at nvis at all but an amazing dxer.