Sotiris, what do you mean by change your old posts over into the block format? Does this show up on your live site? Also, do you think by not changing it over it could affect SEO?
I just mean it will change them back to the old editor format. I am not a big lover of Google and its updates, So I don't really put that much focus into SEO I mainly use social media and email. Maybe if you ask that to someone who is really into SEO.
Quora would be a good place to ask as there are lots of SEO experts there. :-)