A fundamental question about filter phase response effects
We know that adding two sines with same amplitude but with different phases will yield a sine with less than twice the one of the two amplitude.


You forgot to say "at the same frequency". Since your two components are not at the same frequency, this doesn't necessarily apply. 

A delay that causes 15 degree change in the phase of the 400 Hz signal is only a 0.0015 degree change in the phase of the 4 Hz signal.

The overall amplitude of your signal won't be noticeably changed.


  So even a filter is extremely flat in passband, the phase response seems will corrupt the output signal shape in time domain.


Yes, the output shape will be slightly changed.

You could plot the signals in a SPICE simulator, or Matlab or whatever to see the effect. Given the 2 decades difference in frequency between your signal components, you'll have trouble seeing the change if you don't know what to look for.


  I guess this will have no effect in frequency domain.


If you consider the phase of the signal as part of its frequency domain representation then of course it will have an effect. It'll actually be much easier to see on the phase-vs-frequency plot than on a time domain plot.


  And seems no filter has flat phase response in passband. Can we say this is important only if we are dealing the shape of output signal in time domain?  Is there a rule of thumb for the maximum phase shift of a filter in passband?


Whether it's important and how much shift you can tolerate depends on the requirements for the application where you're using the filter.

For what it's worth, here's the plot. The upper plot shows a 400 Hz signal summed with a 4 Hz signal, and the lower plot shows the same thing, with the 400 Hz signal shifted by 15 degrees:



Good luck seeing the difference without zooming in to very carefully check the phase of the 400 Hz component at some distinguishable position relative to the 4 Hz component.