You can tell the match at the antenna through any length coax. As I mentioned earlier, the SWR isn't affected by changing the coax length. SWR represents the reflection coefficient and that can be measured accurately without knowing the R±jX values. It is measuring the latter, these R±jX values, where coax length matters.
I have a theory on the use of half-wave coax jumpers.. In my opinion, the radio's mounting bracket is not a reliable RF ground. There is often paint and plastic involved. If the path for common mode current ends at the radio, making that path a 1/2 wavelength long (by using a half wave jumper) puts a high impedance that blocks common-mode current on the ends (at the antenna). It would be like trying to drive the end of a half-wave dipole with a low impedance source ~ not gonna work well. So, if the radio is not attached to further grounding structure, using a half-wave jumper could provide a huge improvement.
If making it a half wavelength puts a high impedance at the beginning of the common mode path, there will be no common mode current. If there is no common mode current, the SWR readings are accurate.
