Would it cause interference?
Not my domain, so speculating:
Space-based nuclear power is virtually always a radioisotopic thermoelectric generator (RTG), which works by utilising the heat of radioactive decay from plutonium, in the form of plutonium oxide.
Since the generation mechanism is thermal, the RTG reaches high temperatures (500C, 900F).
The Webb telescope is an infrared telescope, sensing electromatic radiation in the range emitted by warm objects. The telescope itself is cryogenically cooled to 50K (-223C, -369F), and carefully shielded from the Sun by a large (though lightweight and delicate) shade.
Even electrically-powered systems on the cold side of the telescope are designed for the lowest possible power consumption to minimise heating. The instrument package draws 11 milliwatts of power. That's 1 calorie every 6 minutes 20 seconds --- it would take 6.33 minutes to raise 1 ml of water 1 degree Celsius. You burn about 10 calories (10 kilocalories or "dietary calories") in the same time.
https://en.wikipedia.org/wiki/James_Webb_Space_Telescope
TL;DR: thermal generation on an instrument which must be maintained at an extremely cold temperature is a hard engineering problem.
So many design compromises were forced by not putting nuclear power on the telescope. I really hope it works, but I think the odds of getting much useful science from it slim.