I've bad experience I'm afraid. I was full-time PhD student funded over a decade ago, and fell seriously ill long-term. I wanted to change to part-time (continuing full-time was impossible), but the funding council (EPSRC) wouldn't support this option at all. I couldn't afford to self-fund (no savings and too ill to work), so ended up having to drop out.
Basically check with your funding authorities very carefully before doing this.
I'm now a part-time PhD student in a totally opposed discipline. And funded, thanks to AHRC.