i doubt the Andorians and Vulcans would be biologically compatible even in Trekverse, since they're blood chemistry is so different.
In the VOY episode where Torres fixes a robotic soldier (can't remember the name of the episode), she goes to the EMH for help with the problem and he mentions about how a Vulcan and a Bolian couldn't transfuse blood without killing the patient.
It might be the same for Vulcans and Andorians, though a Bolian-Andorian hybrid may be more likely.
As for the point about interspecies breeding being absurd, I do agree that it is a little far-fetched that humans and species just happen to share enough genetic similarity to produce healthy children. This could go back to the fact that all humanoids came from a single species (a TNG episode whose name I can't remember either). Or when Jadzia and Worf were planning a family (just before she was murdered by Dukat), she had to undergo ovarian-resequencing therapy in order to conceive.
Just a few thoughts.