Not really, Brazil become Independent (And have previously It had been elevated to kingdom status while the royal family fled there ) because the liberal elites who took over Portugal after the Napoleonic war and because the absence of the royal family wanted to demote Brazil to the level of a colony again And Also "In light of the wave of conservatism led by the Holy Alliance, the Emperor used his influence over the Brazilian Army to dissolve the Constitutional Assembly, in what became known as the Night of Agony. On his own authority, he then issued a constitution that concentrated the executive power on the Emperor himself (eventually crowned "Constitutional Emperor and Perpetual Defender of Brazil")." (
https://en.m.wikipedia.org/wiki/History_of_the_Constitution_of_Brazil)
I don't think you can simply sum up the Brazilian independence as simply a conservative reaction against Portugal's liberal movement. Pedro was pretty well known for his liberal views, and certainly there were liberal undercurrents among the Brazilian independence movement as well. The fight against the constituent assembly was more of the assembly's desire to clamp down on the possible powers of the Brazilian monarch, it was not a situation of Pedro turning into dyed in the wool conservative or reactionary by desiring more power for his position. Even in the end, the Brazilian monarch obtained a unique position as a moderator between the executive / legislative / judicial... he didn't exactly make himself an absolute monarch.
This is a man who sought to place his daughter on the throne of Portugal as a liberal figure head, even if admittedly his idea of marrying her to her uncle Miguel the archconservative was not a great idea. Same in regards to the break down of the dual monarchy established previously: there were Brazilian deputies present in Portugal, thought their numbers were small and they were mistreated. In some instances, they did work together with liberal deputies to frustrate some ideas during Portugal's attempt to draw up a new constitution that would reduce Brazil's position.
Even if Pedro sought to create a new constitution to increase his own authority, he was still leading a rebellion against Portugal: by virtue of the settlement of the Congress of Vienna and the standards set by the Holy Alliance as a bastion against revolution, democracy, and secularism, Brazil would not exactly be an ideal candidate for such an alliance. Plus, you've still got to address why a South American monarchy (with close ties to Britain) would have any interest in joining an alliance of Prussia, Austria, and Russia. They aren't in any position to be of any aid or assistance. Even Spain joining this Holy Alliance doesn't exactly justify Brazil's participation: why would Spain ally with Portugal's newly independent colony in an attempt to retain their own?
Even if the Holy Alliance wanted to send troops to South America, Prussia and Austria don't exactly have the naval capacity to be much assistance there. Prussia's navy was practically nonexistent, and Austria's mainly consisted of former Venetian vessels: many which were sold off due to Austria's financial issues. The first Austrian ship to cross the Atlantic wasn't even until 1817, when the Archduchess Maria Leopoldina was brought to Brazil. Russia definitely has more naval capacity, but mostly concentrated in the Baltic and Black Sea (and c. 1815, it was essentially bottled up there, as no warships are allowed through the Bosporus straits). Spain can be of more assistance, but they can't transport their own troops plus others.