For me, learning the woods im going to be hunting and what the birds are doing is more important.
Get out and scout.
That. The only challenges I could imagine with later season vs. earlier season are 1) it's a lot hotter, so it's a comfort /patience issue with being able to sit in 90degrees [in Florida] and 2) by the law of averages several birds have been shot and more have probably been shot at. They're spookier, but the cycle and hen availability could have the birds stirred up.
I've heard turkey gobble on Christmas Eve and on Memorial day, but our season is mid-march through most of April.
If you know the woods and can pattern the birds, it's a lot easier to lure a turkey from 50 yards to have a look than call him from 600 yards.
I probably spend more time scouting than hunting most years, depending on schedule