Is there any Barca young players go on loan and successfully return to become great at Barca? Pique comes to my mind but that is not really usual thing
Arda Turan.
Just kidding, there is nobody from the current squad. But, these players have either gone out on loan or been sold with buyback options in the last 5 years or so from Barcelona.
Adama - Sold for profit and not activated. Turned into good attacking player linked with return here and Liverpool
Munir - Had a good season at Alaves. Returned here but was not impactful. Sold/Released to Sevilla
Cucurella - Turned to solid LaLiga player. Sold for very small profit.
Miranda - Loaned to Shalke. Not looking positive for a Barcelona future.
Todibo - Loaned to Shalke. Looking like we can sell for profit. Not looking Barcelona quality.
Marlon - Loaned to Nice. Good season and sold for profit to Sassualo.
Palencia - Loaned to Bordeaux. Not deemed Barcelona quality and sold to St Etienne.
Denis Suarez - Loaned to Sevilla, then sold to Villarreal with buyback. Impressed and bought back. Sold to Celta after not making it.
Rafinha - Loaned to Celta. Come back. Eventually sold.
Gerard Delofeu - Sold to Everton. Brought back. Sold again.
From above we can see that none made it at Barcelona. But loans gave an opportunity for them to get minutes and develop. Some impressed enough to return to Barcelona and others were sold on after evaluation. These are just off the top of my head and I am sure there are more players.
I think loaning Puig can expedite his options and development like the above.