Large can mean 50 GB to some, 50 TB to others. How long is a piece of string? You need to test some of this in a lower environment. We only migrated a 100 - 200 GB database, can't remember the exact size but still took some time. If the size and migration interferes with any maintenance type of window you might have, you can look at Sybase Replication Server as it used to support heterogeneous replication from Sybase to SQL Server. And I know nothing else at all about it. You would need to research that one. I don't know what it supports these days in terms of versions, other platforms, etc.
Some stored procedures needed to be redone just due to different optimizers on different platforms but that's to be expected. The best way to tell is to test. Issues can often vary with different migrations as well so the best thing to do is to test. And lastly, thoroughly test.