When Great Britain brought its land and naval forces to the American shores to enforce its rule there, before and after the American's declaration of independence, Great Britain's motives seem clear: if it allowed dissent by the Americans, other colonists elsewhere might be emboldened to consider breaking ties with the King. However, in dedicating troops and ships to the Americas, Britain left gaps in its imperial defenses that other nations and their navies could take advantage. Ultimately numerous challengers to British naval supremacy used the American distraction to pile on with their own attacks on British ships and assets, essentially becoming a world war, continuing even after the War of 1812. Is there any record that this risk was evaluated?
It was a former Prime Minister, William Pitt the Elder, who understood the cost and warned in Parliament:
"I know that the conquest of English America is an impossibility. You cannot, I venture to say it, you CANNOT conquer America... You may swell every expense, and every effort, still more extravagantly; pile and accumulate every assistance you can buy or borrow; traffic and barter with every little pitiful German Prince, that sells and sends his subjects to the shambles of a foreign country; your efforts are for ever vain...devoting [the colonists] and their possessions to the rapacity of hireling cruelty! If I were an American, as I am an Englishman, while a foreign troop was landed in my country, I never would lay down my arms, never! never! never! ..."
Pitt also understood how bitterly the Americans (and later the Vietnamese) would fight.
"The poorest man may in his cottage bid defiance to all the forces of the Crown. It may be frail — its roof may shake — the wind may blow through it — the storm may enter — the rain may enter — but the King of England cannot enter — all his force dares not cross the threshold of the ruined tenement!"
Lesser men failed to believe him, and paid the price.
Put another way, the risk was (fairly) "evaluated" by Pitt and not understood by others.
I think this question could serve as the basis for a significant paper. Working within the terse confines of H:SE, I'd argue no. (Research to support this answer would be very time consuming, so I'll offer a low quality opinion rather than a real answer.)
Britain's government didn't have a department of colonial affairs. Britain hadn't had an empire for very long and didn't have the bureaucracy to conduct the kind of risk analysis you're asking about. In order to evaluate the risk they would have to assemble information from the Admiralty, the Army, a non-existent colonial bureaucracy, Colonial Governors, etc. That bureaucracy didn't exist. The British Empire is dated from the end of the Seven Years War, which was less than a generation in the past.
Britain would have had to have a policy. In the absence of a policy, Britain would have had to have a coherent set of assumptions about the relationship between the colonies and the government. That didn't exist. Parliament still hadn't worked out the notion of a loyal opposition, and the notion that two people could disagree and both be loyal was viewed with great suspicion.
Arguably Parliament fell twice due to issues related to how to manage the colonies. If you accept this argument, then it follows that colonial management was a "wicked problem" - the predicted outcome could vary significantly/discontinously depending on which assumptions you held, and there was no body of evidence against which to test assumptions. Personally I believe that Parliament's actions were motivated by questions about Parliamentary sovreignity and control, and that question about colonial affairs were secondary. If I'm right, that would mean that the risk analysis would be carried out on flawed assumptions.
Serious divisions within the British populace about what was right and wrong. This would require a lot of research, but I've read multiple histories that mentioned that there were significant stakeholders very sympathetic to the American cause. Pitt, Lord Cornwallis (the Naval officer, not the Army officer) and possibly much of the London middle class.
Remember that almost all the American revolutionaries did not intend revolution - Rebellion developed as the accidental result of gross missteps on both sides. Difficult to conduct a serious risk assessment about the consequences of revolution when all parties insist that the goal is not revolution, but merely a restoration of the rights of Englishmen.
All the above points are arguable, and none of them are directly provable from primary sources - I'd have to dig through secondary sources and opinions to build a case for each of the above points, and SE discourages that level of original research.
From the very beginning the revolt in America was closely connected with British-French wars. France supported the revolt, with explicit purpose to harm Britain, and of course this was very well known to everyone: major fighting happened between the British and French naval forces in American waters during this war. So most certainly British did understand the risks.