I would absolutely share the diagnosis you have, and equally to share any concerns you may have about that diagnosis.
I have to say that most people can't tell my DD is on the spectrum either. Heck, plenty of professionals can't tell that she's on the spectrum. But that doesn't change the fact that she IS and knowing that she is, or might be, or whatever, that does help professionals think about how best to deal with her.
If your child had a speech impediment that was mostly re-mediated now, but still lead them to be sparse with their words (particularly with strangers) and possibly to be fairly non plussed by therapeutic type situations - would you tell the tester that? Because telling might lead them to correctly realise when a little extra prompting was warranted, lead to better answers and a more accurate score.
Providing the tester with all relevant information allows the tester to provide you with the best quality results they are able to.
