There have been a few discussions on invisible thread and the consensus seems to be that many brands will become brittle over time and break. I've only ever used it in wall hangings and the odd seam - mostly to anchor a particular area in appliqué. I'm sure someone will be able to recommend a brand that will stand up to repeated washing.
As it's name suggests, it's also very difficult to see and although any mistakes might not be too obvious on the front, they may be more apparent on your back.
Personally, I would use a variegated such as King Tut as their colour change is every inch or so and I feel the subtler shades blend well, yet the brighter ones are very effective. Good luck!