Doty’s should be in Mayflower Society "Silver Book.”
There’s a profile for Martha (not Sarah) Doty married John White here:
https://www.familysearch.org/tree/person/vitals/L6LL-1LM
With a comment:
There are two women named Martha Doty being mixed up with each other. This Martha Doty was born in 1672 to Thomas Doty & Mary Churchill. She married John White. (Source: Mayflower - Births & Deaths - Vol. 1 & 2)
The other Martha Doty was born on 9 July 1671 to Edward & Sarah Doty. She married Thomas Morton. (Source: Massachusetts - Town & Vital Records - 1620-1988)
I do not see a child George White listed for this Doty / White.
It’s not significant to me that no one has found a vital record for birth as yet. Sure, he could be a new immigrant from England - turned Patriot? Really? From Ireland or Germany would make more sense - but the children names don’t suggest that, particularly. Where does the name “Archilus” come from? Are there probate records in Connecticut? His town associations? His childrens?