I think that even if it had passed not only the Continental Congress but also British parliament with flying colours, it could have been only a temporary solution to the problem (parliament legislating on behalf of colonists without them having a say in it, and deliberately hurting/doing things perceived to be deliberately hurting the colonies).
If you read the plan
here it says the following:
That the said President-General and the Grand Council, be an inferior and distinct branch of the British legislature, united and incorporated with it, for the aforesaid general purposes; and that any of the said general regulations may originate and be formed and digested, either in the Parliament of Great Britain, or in the said Grand Council, and being prepared, transmitted to the other for their approbation or dissent; and that the assent of both shall be requisite to the validity of all such general acts or statutes.
That in time of war, all bills for granting aid to the crown, prepared by the Grand Council, and approved by the President General, shall be valid and passed into a law, without the assent of the British Parliament
If I'm reading this right, this tells us that, except in a time of war with bills granting aid to the crown being passed, all bills can only become valid legislation after they are approved of by the Grand Council, AND Parliament, and also the King himself to grant it royal assent. Considering Parliament in Britain is heavily influenced by British commercial interests, which is why they did things like suppress manufacturing in the 13 Colonies to avoid competition with British manufacturers (everything from steel to
hats), anything that results in the interests of the colonies and Britain diverging like commercial matters could result in the British parliament pulling a huge hissy fit and dragging their feet all the way across the Atlantic. I imagine such a scenario would not be fun.
Actually, what legally even happens to the Hat Act if the Galloway plan of union passes? Surely it's still in effect since America and Britain are in a full political union, and if it counts in America the Grand Council will need to pass another act to repeal it. I'm not sure how the law would work in that case. Even if something like that isn't a problem, a lot of American advocates of industrial development (like the federalists and onwards) were big advocates of tariffs to protect America's industrial development, so the Grand Council being run by Americans will probably try to stand up for America's economy. Even if the king is willing to rubber-stamp it, will Parliament give assent to it?
Maybe Britain would need to pass something like the Statute of Westminster 100 years early for America, or maybe Americans would still get angry with parliament later down the line and the Grand Council could unilaterally declare its own separation from Parliament (could America still technically remain under the King?). Surely there would be too much friction for Britain and America to remain conjoined Siamese twins forever, either centralisation or centrifugal force has to win out eventually.