It is a good idea but a little late. It this had happened five or ten years ago it could have lead to a standardization of web-browser code. As it stands now, if I wanted the source code to a web-browser I would stick to WebKit or Gecko.
This company is a new company, and I personally am paying a lot of attention to it having been a hater for a long time. The latest IE is a decent effort if you leave out Bing (which remains awful) and open sourcing it should be encouraged and applauded if it were to occur. As much as I love Firefox, IE is in my experience a far more stable and credible long term competitor to Chrome. For an example of some of the unsung quality behind IE, it is the ONLY browser that sends SVGs to a printer as vectors and not a screen-raster rendering. This is a small detail but points, to me, to the underlying quality that IE represents. For other Microsoft doubters: typescript, or the almost single-handed effort that Microsoft has put in to defeating large botnets.