My EA iAmp800 provides this feature; it's great to be able to push a button to engage/disengage the EQ section. That said, I've never seen a plot that shows its frequency response with the EQ section bypassed, so I can't claim it's truly flat in the bypass mode.
Had my iAmp500 hooked up to an analyzer yesterday. Utilizing bypass, it was flat as a board from say 8khz up to 15khz and then dropped off. Seemed to have a hump in the bass around 100hz. Bass is hard to read since it jumps around so much. Tried averaging and the hump still seemed to be there. With bypass switched off, about 8khz and above seemed to drop off a db. I'd attribute this to the extra resistance from putting more electronics into the path.
That bass hump seemed to 2-3db and then dropped a db just above it, but above that, everything seemed to be within +/- 1db.
Please keep in mind that this was not a lab quality setup, just software on a laptop. The software itself and the low quality of the soundcard I'm sure influenced the output.