without a spectrum analyzer, just wondering if a piece of coax cable draped across an AP would cause interference or RF distribution problems. I say yes it could. Other's I have talked to say no. Thoughts?
There are many variables here. It would partially depend on the signals and frequencies present, in both the cable, and the AP. But would also depend on the "quality", meaning % coverage, of the braid on the coax. The poorer the coverage, the greater the RF leakage. Too strong an RF field from a leaky cable could also deaden the sensitive radio in the AP.
More likely the coax shield, because it's grounded, will disrupt the AP's (antenna) RF pattern and therefore affect its range. This is very similar to Ham Radio installations where operators are advised to not place their antennas near anything metal.
In addition, the internal RF cable routing inside a wireless device is very important, and even the slightest deviation from the correct route can reduce the range, of say a handheld printer, from more than 100 yards to less than 30 feet. That's using the same radio, antenna ,and cable but the cable has slipped out of its preferred routing.
This can happen for example, where "commodities people", who have no RF knowledge, try to use the same length coax in three different sizes of handhelds. The excess cable in the smaller units gets looped around all sorts of components, totally destroying its range. A left handed assembler will likely fold-in the cable differently than a right handed one - really bad for consistent performance. The smaller the model, the worse the effect.
I've literally seen this happen dozens of times, in dozens of models.