Too late for that, that is way before the ACW. That in and of itself would butterfly too much for the ACW to be anything close to OTL . POD is stated to be May 1864.
Eh, while that may be the case Guatemala and the rest of Central America wont offer anything nearly as promising as a densly populated California. Adding more land that wouldnt accept a loss of soverignty very well along with the ongoing Maya revolts would make the venture not worth it. Forgive me for ignoring the stated POD but it offers something way more plausible than "Maxie cuddles with the poor and Liberals".
If a foreign imposed polity is to last in a hostile land one of the two major parties of the time has to be drawn into the tent, and fully use its political program. As the Liberals weren't ever to the best of my knowledge yearning for a monarchy in any form, the Conservatives have to be used. They certainly were OTL, but Maxie's mild Liberal streak kept them distanced on some matters. Even if L. N. were to find a willing noble or scion of a dynasty that didn't do such things as offer Juarez the position of P.M. or not restoring some (or all) Church lands, a real problem is still floating and needs to be addressed, the economy. Continual warfare and unrest through out the previous few decades didn't do wonders for the development of a middle class, or a rural population that weren't de facto peons in bonage. How would the Empire deal with this immense issue? I am certainly not a wizard at the finer points of the Liberal and Conservative economic plans but from the bit I know on the latter, they wouldnt have anything to really alleviate these issues. Even if they did, there is still the related issue of a horrid budget for the Imperial regime. As a side note, my constant mention of the sale of church lands started under the Liberals and continued under Max was done by the Habsburg because his tin pot Empire needed the money, badly.
I will ever understand this fascination with a regime that fell apart once the Gallic muscle behind it left. Its sole dynast wasn't what was expected from the local politicians willing to work for the regime, what could one expect if the monarch expresses admiration for their long time political rival (and at the time lead rebel). It had a fairly pathetic military, never trained and armed as effectively as perhaps they could have been. The Empire sorely needed sources of income, but this can be said of the rebels as well. Just having this polity exist past its timely destruction is a wank, at least to me.