Upvote:1
As this type of information is indeed not available online and, even if it were, its reliability would not necessarily be too great, I can't fully vouch for my response... but, I'm convinced that, yes, it will be possible to travel from Rio to Ilha Grande on January 1.
I live in Brazil and there is not one day in the year that public transport doesn't run. To get from Rio to Angra dos Reis, you can take a scheduled service from the main bus station in Rio, or you can travel via local, slower, but frequent, transport.
The boats from Angra to Ilha Grande are speed boats that don't run on a particular schedule. I'm sure that plenty of Cariocas go to Ilha Grande for the new year, meaning there will be a need to transfer people back and forth, also on New Year's Day.