it is not necessary to upgrade, no; the database backup is the same, regardless of service pack, version, and that's what you would backup/restore. the service packs / CU change how the engine behaves, and not how the backup is stored.
one thing i'd mention is to make sure you update statistics; the stats are used differently between engine versions, and not updating statistics often leads to reports of "the new super server with 40 petabytes of RAM is slower than the old server" until that is done.
something like this is what i've suggested int eh past:
DECLARE @Exec VARCHAR(MAX)
SELECT @Exec = ''
SELECT @Exec = 'UPDATE STATISTICS '
+ ' WITH FULLSCAN ; '
+ CHAR(10) + @Exec FROM sys.tables ORDER BY name DESC
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