A wireless charger has no data transfer capability yet, so "no" for now. However if a USB port shows any sign of data transfer capability, it's blocked until you trust it.
Power starvation / observation attacks are passive attacks in a sense. They get their results by observing only.
The article is about a side-channel attack, where you don't transfer any data, but just observe something (in this case power draw from a wireless charger) to get some information.
In these types of attacks, you don't transfer any actual information, but guess something from observation.
There are more exotic attacks [0][1] which exploit the heat computers generate to exfiltrate data or time power starvation attacks.
If your device is locked, you need to authenticate to trust to said device.