Very questionable! Immigration and dates assume that this is indeed the William Wright with Gage's troops at Bunker Hill and that he had a child very young. I do not have that connection except for B&L notes that say "father Wm." and "father fought Bunker Hill".
Possibly the Wm Wright b 17 Sep 1758 on Bishop Gate St. in London England & he came to America with the British Troops under Genl Gage & after the Battle of Bunker Hill he deserted from the British Army joined Colonial Army (Berkely Co. VA) and ended up in Pulaski Co. MO -- but he would have had to have been dad at 14 or birthdate is off. Actually, Gage and been in the colonies for many years, so that is not quite right, but he was based near New York City as commander-in-chief, that would have explained Rachel's birth in New Jersey.