Currently you don't have a diagnosis. So your first decision is to decide whether to get an assessment. If you decide not to at the moment, you can always change your mind later. I suspect that if you did go for it, it's the sort of service which might not happen very quickly, especially now. So if you decided to go for it today, you might still have a long way to go before you would have anything to tell an employer. Although you cod tell them you're waiting for an assessment.
If you did go for an assessment and received a diagnosis, that's when you will have a choice over whether to say anything to work.
In my case, I discussed it with my GP. He pointed out that there are people with autism who need a lot of support from different services to just live, and I'm not like that. He's not keen in labelling people unnecessarily, but he would refer me for assessment if that was what I wanted. He didn't think I could be autistic because I could look him in the eye. (The man has looked at my vulva before, I'm past shyness there.)
I realised the main reason I was thinking about it was because my manager was being an arse, and I was feeling under attack because of that. I shouldn't need a diagnosis, because what really needed to change was that he needs to accept not everyone thinks the same way he does, and people should still be listened to if they aren't neurological, or if they're the only woman in the team, or whatever his problem was. (We're a unix system administrator department - a natural home for people with autistic tendencies, I'd say.) And some months later, when I was still wondering if I should push for it, because a diagnosis could give me some protection at work, the department got reorganised, and I got a new manager and life is better (in that sense, anyway.)
But unlike you, I don't have children. If I did, and they had been diagnosed, I would probably be going for anything which might help me understand them more, even if in the end it didn't help, because then I would at least know I tried.