Not competing with Fati.
Koeman wants to play Depay-Aguero/Fati-Messi upfront
So most likely he will take Kun's place when he returns
Exactly.
Koeman utilised Memphis as a centre-forward during their time together with the Netherlands national team. Pretty sure he plans the same at Barca if nothing goes wrong with Ansu's recovery. If he has another relapse this can change everything though. He'll have to run more off the ball than he did previously, so 65/70 minutes Memphis per game with Aguero being his sub seems a useful possibility.
During Koeman's time as coach of the Elftal, Memphis has played in 18 out of 20 games. The other two he missed due to an injury.
In 16 of these games Memphis played every minute. 16 of the games he started as CF, two as LW. He scored 11 goals and had 12 assists in 18 games under Koeman.
Now I know that national team football is a bit different, but it looks like Koeman knows how to use Memphis and how to get the best out of him.
His haters will say that Memphis failed at Manchester United and how he will never make it a big club. His coaches were Louis van Gaal and Jose Mourinho there, so I have a hard time taking that against him. He matured a lot since then too.