Acceleration thought experiment

[Zula110100100]

In the thought experiment about the laboratory at rest in a gravitational field and another at a constant acceleration, could one not tell the difference by firing light of a known frequency from a height above you, in the gravitational laboratory the light would get blue-shifted, while in an accelerating lab you would get redshift? is this the case?

 

[pervect]

Both would get blueshifted.