Is the current through the MCP41010 digital potentiometer independent from its supply voltage?
No, it’s probably not ok. Most digipots will not tolerate more than a few hundred milli volts on the pot pins outside the range of the power supply pins so, if the supply is 0 volts and 3.3 volts, you should not apply voltages less than -0.2 volts or greater than 3.5 volts to the pot pins without referring to the data sheets.

The wiper limit of 1 mA is in addition to the above maximum ratings.

All digipots are not the same so always refer to the actual device’s data sheet.