Yes, you will still need to have it plugged into the wall. The pump doesn't receive its power from the Apex. The variable speed ports only use a low amperage signal to indicate pump speeds depending on the level of voltage. Data in other words, just very simple data.
As far as testing the cable goes, I would set up a profile to have it go from 100% power (or 80% for the 6055) to 0% power (off) alternating every second. If, after configuring the profile to the correct variable speed port, the pump doesn't respond like it should, then you know your cable isn't wired correctly.