Discussion with my friend: He plays carry. We get the first blood mid near first bounty rune.
He leaves the fight on 100 hp and decides to suicide himself to the enemy tower or Pos 4/5 to get back to his lane quicker and regenerated.
Is this the correct play?
Yes
First blood gives a fair amount of extra gold so a 1-1 score is a net benefit to whoever got the first blood.
The regen the HP and MP that were spent for a first blood is likely to cost ~150g, which is basically a whole wave + a trip for a level1 courier that is easily sniped. By giving the enemy support the bounty and getting a free TP for getting killed, the enemy can at best get some extra regen but the carry does not need to pay the regen cost. The exp on level1 kill is negligible.
The biggest issue of suiciding at level1 is that it worsens KDA and that depending on your skill bracket, your team will criticize you for doing so.