I doubt an ITIN letter proves anything relevant. If you have filed a joint tax return, then the tax return (or return transcript) would be useful evidence. But the fact that you have requested or been issued an ITIN doesn’t—you would also have an ITIN if you were filing separately. The only evidentiary value of the ITIN letter that I can think of is that it places you at the address on the letter, but presumably you have lots of other evidence that does that.
As for delays, I think it generally depends on what stage the case is at. If an officer is just about to make a decision and sees that there is unsolicited evidence, they have to delay any decision to review the evidence—and may decide to put it off and look at a different case instead. But if believe that you are many months from a decision, based on processing times, there’s probably not much of a delay.
