Plugged into shore power and starting the truck...?

Short answer: no damage could be done

Long answer: it's all 12VDC so no damage could be done. Since your solenoid is from a keyed source, I'm assuming that this keyed source is not powered while in the starting position (similar to how the heat/AC blower does not run while cranking).

Even if you were on the factory trailer wiring 7pin. The charger on the TC cannot pass enough current through the wiring (the truck batteries will carry most of the load) during starting. The circuit breaker on your firewall would open if there was too much of a load on the wiring anyways.

You're fine!

Thanks for the info... all sounds good except that I am not using the truck's factory 7-pin. I wired direct a 10 gage cable with a continuous duty solenoid- the 12V on/off from the ignition source is fused. Am I still OK? This is my set-up going to the TC:

No, you're fine. There are too many safeties and limitations involved to do any damage.
* The factory wiring from the TC to the truck can't pass enough current to do any damage, at least when compared to a stout set of jumper cables.
* The truck has a fuse on that circuit, and the highest I've ever heard of is 40amp, most are 25-30amp. Your converter is likely 45 amp.
* The circuit is de-energized in the "Start" and "Accessory" positions, so it can't make the connection during start up.