Answer
Yes, it would have an effect.
Work Step by Step
If the energy spacing between 1 and 2 were equal to the spacing between 2 and 3, there would be only two unique spectral lines.
A transition between the n=3 level and the n=2 level would emit the same-energy photon as a transition between the n=2 level and the n=1 level.
The other spectral line would be due to a transition between the n=3 level and the n=1 level.
