No. Log chain and restart recovery are UNRELATED.
An intact log chain gives you the ability to restore a database to a particular point in time, in the case of a disaster (eg a disk failure)
Restart recovery (databases 'in recovery') will run every time a database starts up and it cannot be prevented. It's essential for SQL to run it always.
They are totally different concepts, totally different reasons, totally different operations.
There are several reasons why you may have a slow restart recovery. None are linked to backups.
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability
We walk in the dark places no others will enter
We stand on the bridge and no one may pass