The Justice will join the Court’s deliberations as soon as sworn in, whenever that is.
Although justices don’t usually rule on cases they haven’t heard in person, it has been done before because the paperwork and transcripts contain all the information anyway.
This session’s cases are long ago locked in. Future cases are OK’d anytime four justices agree to hear them, but they are almost always scheduled far into the future.
Thanks for the info! :)