Well, the US was not perfect, but it became the first time in history when people actually stood up against the oppressors and fought for the Rights of Man and hence it did inspire people around the world. Besides, the ARW in one way or another led to French Revolution, which spread radical ideas of equality and liberty, as well as nationalism. Also because of that, the US also became the land of opportunity for lower-class Europeans who were oppressed by European monarchies àn nobilities.
After all, the US and later France were the world's only democracies during the 19th century (Britain should not be considered as a democracy until 1928).
Well, the bottom line is that until 1914 only a third of British male adult population were eligible to vote. Meanwhile, all US white males could vote since 1860.
Racism was common during the 19th century. For Britain, we cannot conclude like that because there weren't a lot of people of other colors in the UK.
Honestly, do people still believe all of this guff?
The reality is, by modern standards none of these countries were proper democracies - in fact few nations in the world were (if any).
Britain at the time of the ARW was far more liberal and democratic than most European nations, with parliament holding power at the time, which it had done since the Bill of Rights was enacted in 1689 - a century before the US version. In fact the Republican institution that the "founding fathers" implemented, that exists to this day, was set up to be largely undemocratic, and ensure domination based on wealth. Lest we forget most of them were slave owners. Indeed the core principle behind the ARW was not the poor oppressed man in the field not being given a voice, but the landed gentry of America being expected to pay taxes to support Armies in north America without representation before the King - something that harked back to the
English Civil War 150 years earlier.
The French revolution was undoubtedly influenced by the ARW, but America losing this war does not butterfly it away - the fervour for reform in Europe already existed, and France was already in financial difficulties after the 7YW - the ARW just made things worse and ensured that the Estates General would eventually be called.
As to 19th century democracies, Britain steadily became more democratic as the century went on, particularly the reform acts of 1832 and 1867, and the secret ballot in 1872 - the US would not follow for another two decades. As to the French, well they went from Empire, to constitutional Monarchy, to Republic, back to Empire and back to Republic again. Universal male suffrage came in in 1848, but by 1852 they were an Empire again.
Anyway, as to the original question and linked to the above, the general anti Monarchic pro liberal democracy movement was in effect and gathering pace in Europe in the 18th century and continued into the 19th - the ARW was both a product of that and an influencer. Even if you have the ARW fail, the initial grievances are still there and need to be address - so you'll still end up with a semi-autonomous dominion long term at the least.
Beyond that it's really hard to say, but of course within 100 years the other dominions were all but independant any way, so who's to say that the US might not have ended up going a similar way anyway?