If I can extend your question out more broadly to pro-Democracy groups in the 1830-1850 period then we can say that certainly the British Chartists did use the United States as a symbol of freedom from tyranny, and an example to show that democracy was not just a utopian ideal.

In a way, the British Chartists and the 'America' of the revolution had a common enemy - the tyranny of the British upper classes/royalty.

Certain members of the British Chartist movement even recommended in writing that those similarly minded should emigrate to the United States to escape this tyranny. Unfortunately this view of the US was a little bit rose-tinted, as many newcomers to the fledgling nation found themselves disillusioned and at the mercy of capitalist overlords, in lieu of noble ones.

But that goes beyond your question - the idea of America, moreso than the contemporary reality of America in the 1830s and 1840s - was a powerful and recognisable symbol for Chartists.