@Jason Griffin good question, and smart to ask before you find out the hard way.
The short answer is I wouldn't assume it's safe to have both rails active simultaneously without confirming how the power path is managed on that specific board revision. The concern you're describing is real — if the supercap output and USB VBUS are both trying to drive the same rail without proper isolation (a diode OR arrangement or a proper power mux), you can get backflow current or voltage contention that at minimum causes unpredictable behavior during the flash cycle and at worst stresses components over time.
The STLink programmer interface on the Power/Program Kit is integrated, so Moamen would know exactly how that handoff is handled — whether there's automatic rail switching when USB is detected or whether you need to manually disconnect the supercap side before programming. I'd shoot a message to support directly to get the definitive answer for your board, rather than guessing at it.
In the meantime the safest bet for your field logger build is to drain the cap or physically disconnect that output before any programming session, just until you have confirmation on how the power architecture handles it.
