Can SQL Server 2016 log files be applied on SQL Server 2012 This is in relation to a rollback scenario from a 2012 -> 2016 upgrade.

The scenario is that the SQL Server 2012 database is restored onto 2016 and log files applied until it is up to date. Then production systems are cut over to 2016.  Database is kept at compatibility level for 2012.  Subsequently, incremental logs from the 2016 instance are kept until the need to roll back (let's say 8 hours worth).

Can the logs now be applied to the SQL Server 2012 instance to bring that up to date?
No we won't be able to do that. This is because the internal file structure is different.

You can use third party tools like SQL Compare and SQL Data Compare to do "diffing" between your source and target, generate update scripts from those differences, and then execute those scripts on the target platform; this works across different SQL Server versions.

I hope this helps