It's a sketchy, well argued topic. TIG, MIG? High frequency commonly used in the TIG process is a cause for concern.
Just for instance, welding on a fuel injected car.... You have an ECU with delicate electronics, just like your CNC will have, and people weld every day in the engine compartment... I'm leary about TIG welding on a vehicle, again, the HF. I've never had a problem MIG welding though, just disconnect the battery and don't worry. But I have customers who claim they have burned out thier ECU by MIG welding without disconnecting the ECU. It could be they did something like improper grounding, hooked the ground up WAY too far from where they are welding, or used it as an excuse?
One thing though, a lot of times magnetic fields created by welding and HF starts and or backgrounds with TIG welding can damage electronics today, they may not fail until next week. Same goes with static dischage when assembling electronic components.
Is it a good idea? No. I'm sure CNC welders are made with all of these issues in mind, properly grounded, shielded and isolated circuts.
If you have the option, do the welding somewhere else, it's your safest bet.