Yeah I think undervoltage is probably less of a concern. I’m not an electrical engineer, just an embedded systems software engineer, but I’d imagine if the push is designed well it just won’t power on like you said.

One other side note, the default voltage for all USB PD connections is 5V, although it should quickly negotiate something higher.

If you want to give this a go, I’d recommend picking up an in-line USBC to USBC power meter. So can can keep an eye on things. I’ve got this and it works well: https://www.amazon.com/MakerHawk-Voltage-Current-Multimeter-Voltmeter/dp/B07NXRPNPR/ref=mp_s_a_1_16?crid=J5BNYDMSD3HK&keywords=usb+c+power+meter&qid=1687555175&sprefix=usb+c+power+meter%2Caps%2C159&sr=8-16

If i’m right about how the cable works, you could plug the cable in through this meter, see the voltage jump to 20V, and then be fairly confident your Push is on good hands.