Hiya. I don't really post much other than on the TH thread, but your little boy sounds so like mine that I had to reply, even if only to try and reassure you a bit. I think you are roughly where we were a year ago.
DS is now nearly 3 and a half. At 2 he was barely talking. At 2 and a half he had a vast vocab of words, but they were all nouns. He labelled stuff, didn't communicate with us, didn't ask for food/juice etc. In fact, he had never put 2 words together. People would say, oh I'm sure he understands everything. He didn't.
We were the ones pushing for help etc and had plenty of professionals telling us to 'wait and see' and that he was still within normal ranges for stuff. Anyway, we asked for hearing checks (which were fine), salt assessment and referral to a paed. Salt also has ridiculous waiting list in our area so while waiting for a triage appointment with them, we began private salt. DS started putting words together and by the time we saw nhs salt, she discharged him saying he looked to be learning fine, just a bit slow. This was despite never actually using his language to communicate with us. 
We were given an autism dx in March. There's been a big push in our area to get waiting times down for autism assessment so it only took us about 6 months. I don't know what Griffeth assessment is but your son can definitely be diagnosed before 3.
My DS is now communicating in full sentences. He now uses language for much more than just getting needs met. He is a super happy little boy and will be starting mainstream nursery in August. Like you, I didn't think he could have done mainstream nursery a year ago but now I know he'll be fine. He is definitely not severely affected by the problems he has. His biggest issue is not responding to people when they talk to him. His receptive language has also improved hugely.
Now, please don't think I'm anti-dx. I really am not but our dx hasn't helped us much. There has been no help or support. The only person we've seen since is the EP who will assess him in August just prior to starting nursery. For us, we really only saw the dx as being useful for nursery/schooling. My DS doesn't have any difficult or challenging behaviours, he doesn't have any stims. He doesn't have a restricted diet. He responds to his name well. He has a good sense of danger. Tbh, 99.9999999% of the time, any issues we have are simply 3 year old issues rather than any caused by autism. All that said, I'm still glad we got the dx. I feel like I've got it in my pocket, just in case I need it at any time. If someone talks to him and he ignores them, I often just say he has a speech/language delay which, for now, works fine. I usually don't tell people he has a dx.
I can't say if your son has autism or not, but if I were you I'd go through with the assessments. There might be better support in your area than mine. Also, you don't have to tell anyone about his dx, if he gets one. It's information that you can disclose if you want/need to. The dx was useful for my PIL, who couldn't see DSs problems. They love him so much they'd make excuses for his language/communication problems. The dx has made them face up to the fact he has some issues and that DH and I aren't just over-anxious parents.
I think this has become quite an epic reply, sorry! But hopefully something I've said might help. 