Is it possible to use the microphone as the input for both arduinos if I split the "input" wire
Yes. The general rule is that it's OK to connect two inputs together, but you should never connect two outputs together.*
...and the ground to go to both arduinos? Or would I need to bridge the ground between the arduinos?
Yes Both need a "complete circuit", so both need a ground to the microphone module.
- This isn't the best analogy, but it's like having one person talk while 10 people listen... That's no problem. But if 10 people talk while one person listens, that doesn't work so well.
With electronics, you can burn stuff up with two or more outputs "fighting" each other. And as always, there exceptions to the rules.