i mean this kindly, if these were regular toddler behaviour then it wouldn’t have come to the attention of the Nursery staff. They definitely wouldn’t have approached you or ask SENCO to assess him either. They see multiple DC every day and they are telling you that the behaviour of your DS is different to the others 
The assessment process for ASD is just that, it’s an assessment. If he doesn’t have ASD then he won’t get a diagnosis.
The waiting lists for assessment are also long so it’s in your interests to get him on the Pathway as soon as possible.
Did the HV do anything other than the SaLT referral?
Did she for instance do either of these assessments:
33 month Ages & Stages
or the 3 year Social & Emotional Ages & Stages?
If not, could you fill them in and score them? There are usually MNers around who can help you understand the scores.
Depending on how he scores, you may need to ask to see the HV again and insist on a referral to a Paediatrician for Assessment.
If the HV wants to adopt the “wait & see” approach remind her that you’ve already been seeing a Private SaLT who has mentioned ASD and Nursery have concerns too and you would like the referral making. If she still tries to put you off ask her to make another appointment for the week of his third Birthday so that she can see how he’s doing then. The trouble is that if you don’t push, he might very well get ignored.
Let us know how you get on with the assessments 