I may be outside of the normal use case here, and absolutely I am giving my opinion so judge it as one voice in 255 million (or whatever gmail's user count is now), but this isn't ever faster for me. I always have a gmail tab open.

As to remembering the source of a piece information, I made no claim to be perfect at this. What I will claim is that for the 95% of the time that I DO know the source of a piece of information I will be annoyed by results that are not from my intended search space.

Obviously Google has a pretty good track record at returning relevant results, but I can still hope for an off/on switch.