Would the skin effect provide benefits or would capacitance/inductance cause problems?
For HF (e.g., 3MHz), the skin depth effect is <50 x 10^-6 m even for aluminum, and it is thiner for higher frequencies, so braid should be fine.
The bandwidth of the J-pole is affected by the diameter of the radiating element. The band is wider at higher frequencies, so to cover the 2m amateur band, you need about the diameter of rg58 shield. HF bands, being narrower, can stand a narrower diameter wire and still cover the band.
Having said that, I've made 20m and 10m j-poles, but I don't think a 160m j-pole is reasonable. :)
RF will flow through the outermost layer of tin, in either tinned copper braid or tinned copper wire. Thus, very little current will actually flow through the highly conductive copper in the center.
The conductivity of copper is much better than tin. Tin is only 17% compared to copper at 100%. Will you notice a difference? The only way to tell is with two different J-poles and a proper test setup.
See this answer about tinned braid vs. solid copper. Note what might happen when the braid gets corroded and the individual wires get insulated from each other.