If I use RG6 coaxial cable in odd multiples of 1/4 wavelength as a serial matching stub, can I also use it, without modifying the length, as a coiled RF choke balun at the antenna feed point?
You can, however the efficacy of the balun would highly questionable. "Ugly baluns" have been shown conclusively to be quite poor at reducing common mode current outside of narrow frequency ranges, as they are self resonant.
The combination of the inductance and the turn to turn and inter-conductor capacitance of the coax creates an LC tank, not a primarily inductive choke. This means that, while you may get several hundred to perhaps a thousand or so ohms of common mode impedance across a narrow resonant range, across most frequencies, common mode choking is minimal.
Ugly baluns must be built with particular dimensions for a given type of coax, and changing from one kind of coax to another can drastically alter the design for a given frequency.
Ferrite baluns are almost always better in almost every way, and can be constructed for $20 USD or so.