When you connect a multi-track tape deck's outputs to the track inputs
of a mixing desk, don't the signals pass through all that complex
processing? Therefore, a plausible DAW implementation could attempt
to do something more than A+B=C.
Of course it's possible and some companies do. But generally if they do they will
model it on a well known and loved analogue desk and have it plastered all over their
advertising in big letters. For example Propellerhead's Record which has a channel
strip based on SSL.
But again, at unit gain input and all EQ flat even desks like this will be designed to be
as flat and transparent as possible. There will always be some noise, there will be some
kind of analogue compression on overdriven signals (rather than digital distortion of
integer math or infinite headroom of floating point math) but the main difference will be
it's a channel strip and the sound of the EQ and Dynamics (compressor) which are
included in the channel strip, rather than the summing involved.