There is a sharp difference in tone. The original version, after the first verse, is not addressed to Jacobites at all, it's just a stream of invective about them. But the Burns version is directed at Jacobites sympathisers throughout, seing them not as enemies to be defeatred but as friends to be won over.

He's putting it together at a time when the Jacobites were history, there was no chance of another rising, because, even aside from any other considerations, there wasn't a viable Jacobite pretender. So the phrase "Jacobites by name" takes on a new meaning - it now means anyone using the name and the sentiments and the rhetoric in a time when the time for that is over. "There are no birds in last year's nests" as Don Quixote puts it, quoting a Spanish proverb.

If you read between the lines you can speculate that he wouldn't have been averse to another crack at the English connection, without the Jacobite trappings, and if there was a chance for victory.

So in no sense pro-Jacobite - but anti-pro Jacobite rather than anti-Jacobite, as the threads title has it.