If you go by the equations, than the mass effect field by altering mass while allowing energy to be the same has to also alter c (i.e. the speed of light). This would suggest that photons that enter an ME field would "speed up".
And yea, the mass of photons (at rest, which is a bit of an issue in itself) is considered to be 0, see here.
One caveat to this is that it kind of contradicts how mass relays work. When we see a ship passing through, the relay becomes active (rings spin up) and cataputls the ship to the receiver. For the comm boyes to work, the relays would need to be always active. Maybe they maintain a tiny corridor but need to widen it for ships? No idea.
You are still right though, von uber. communication at the speed of light is very limited. The light lag from earth to the charon relay would still be 4.6 hours, so your ship from Illium might still arrive before it's message does. 
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