Maybe - but, if so, there's an awful lot of "correction of misinformation" you'd need to do, from the Encyclopedia Britannica downwards. Just looking at the first paragraphs from that encyclopedia, I find ...Wales is a principality, it is same country as England.
Although Wales was shaken by the decline of its industrial mainstay, coal mining, by the end of the 20th century the country had developed a diversified economy, particularly in the cities of Cardiff and Swansea, while the countryside, once reliant on small farming, drew many retirees from England. Tourism became an economic staple, with visitors—including many descendants of Welsh expatriates—drawn to Wales’s stately parks and castles as well as to cultural events highlighting the country’s celebrated musical and literary traditions.
In fact, it seems that the situation has changed fairly recently. If Wikipedia is to be believed ....
However, this definition was raised in the Welsh Assembly in 2010 and the then Counsel General for Wales, John Griffiths, stated, 'Principality is a misnomer and that Wales should properly be referred to as a country.'[120] In 2011, ISO 3166-2:GB was updated and the term 'principality' was replaced with 'country'.[119] UK Government toponymic guidelines state that, 'though there is a Prince of Wales, this role is deemed to be titular rather than exerting executive authority, and therefore Wales is described as a country rather than a principality.'[121]
In addition to repeatedly referring to Wales as a country, Wikipedia has a somewhat different explanation as to why Wales is not represented in the Union Flag ....This is why the Welsh flag is not part of the Union Jack.
There are no symbols representing Wales in the flag, making Wales the only home nation with no direct representation, as at the time of the Laws in Wales Acts 1535 and 1542 (creating legal union with England) the concept of national flags was in its infancy.