Tecniqually, yes.
Historically and culturally? No.
A lot of people in the UK have Irish blood, Irish friends and a close affiliation with Ireland. Most people in the UK consider them as a home nation, despite what happerned in 1922. Technically you're correct, but you're being overly...
You're being very precious on this matter.
Of the 5 home nations, only Scotland have failed to make it into the last 16 of the European Championships 2016.