Not sure why you'd wanna do that, unless you're talking about a tuner installed a long way from the base of the backstay. Some folks believe that using shielded coax "contains" the signal so that little or no radiation is emitted until the center conductor of the coax emerges from the grounded shield.
I understand why they believe that, but I do not agree that it's good practice. First, it does nothing to deal with the very high SWR which can be present along that portion of the transmission
line, and I believe the resultant signal would be substantially attenuated. Some day, it would be nice to model this or to do some serious testing with a good field strength meter.
Meanwhile, if the tuner is located near the base of the backstay -- where it should be -- there's no reason not to use GTO-15 highly insulated wire to make the connection between the tuner and the backstay.
If, on the other hand, you absolutely MUST locate a tuner -- automatic or manual -- some distance from the base of the backstay or other end-fed antenna
, I'd want to investigate the use of a current
balun to transform the feedpoint impedence to something the coax might be happy with, thereby minimizing transmission