If Brazil entered, the US Navy would probably cancel their blockade for a few months to deal with the Brazilian Navy. I don't know how strong Brazil's navy was, but I believe it was largely riverine and definitely wasn't as powerful as the dreadnought-race era Brazilian fleet was, so it might not even take away resources from blockading the South.
And then you realise that Brazil and the CSA share little in common besides their love of slavery and similar economic models. The Brazilian Army is on the cusp of a couple disasters in the early phases of the War of the Triple Alliance, so even if they can make it to the US they could be a bit of a drag on the South. Therefore, Brazil could only give material support, which would have to get past the blockade of the South. But how much material support does Brazil have--or want--to give? For what reason is Brazil supporting the South when they have nothing to gain?
For minimal gains to the Confederacy, Brazil has a lot to lose, though, which could affect them in the War of the Triple Alliance come 1864 and possibly even start tension at home.