I want to know please,

lets say i connect my DVD to the TV with HDMI,
And the home theater system digital in (coaxial) to the TV digital out (coaxial).
I play a movie on my DVD.

Will the sound going from the DVD to the TV and back to the Home Theater System will be 5.1 surround????

This is very important to know, so i would consider how do i wire the entire system (XBOX, DVD, Digital TV receiver, PC)