It is uncertain whether they *went to* the same school.
If *that is so*, it would be catastrophic.

Is this "that is so" correctly used to mean 'if they did' in response to "went to"?

See a translation

If you said this:

I think they went to the same school.

Then you could say ‘if that’s so’

But because you said it is uncertain whether they went to the same school

I don’t think you would use if that’s so instead I would say ‘well if they did go to the same school, that would be catastrophic’

You use ‘if that’s so’ / ‘if that’s the case’ when someone says something that they think they know and you reply with if that’s so/the case


Another example:

I think it’s going to rain tomorrow.

Well, if that’s so/ if that’s the case then I won’t hang out the washing.