Rules help and clarification please!

Me and my friend were playing some 40k recently when we came across a somewhat funny problem:

If khârn is leading a unit of berzerkers, then dies to a precision weapon, leaving the berzerkers without a leader, if khârn then revives (on first death), can he still return to leading the zerkers?

Me and my friend assumed no and played as such but it's still funny to consider if he could. Does anyone here have some concrete rule clarification?