[Oberon]

Hey Gary... I could use a little help here. Have you ever taught a pig to sing?

[Gary Boldwater]

If the cosmic microwave background radiation is "stationary" we can detect motion relative to it in the dipole anistropy: csep10.phys.utk.edu/astr162/lect/cosmology/cbr.html

It all comes down to the nature of space. Is it a vacuum, a fluid or what else? If there are effects produced by motion relative to absolute space then yes. If one could measure the one way speed of light in every direction, this may show absolute motion through non congruent light paths (very similar to the Sagnac effect, except in a linear translation).