I think the AHL general manager's job is less than running the player development of prospects, though he'll have a hand in it, so the answer to your question would seem to be clearly no, but much of the success of an AHL team at development of players and the team's success in the standings is beyond his control.
Among NHL teams such as the Canucks that own their AHL affiliate, the NHL team chooses who does the coaching and provides the team with players who are on NHL contracts, so essentially the prospects and coaches are all provided by the NHL team.
What the AHL gm does that most affects the team's success, both in the standings and player development, is look at the players provided (or expected to be provided) to the AHL by the parent club and fill in the squad with players on AHL contracts. A good AHL GM looks at what his team needs in addition to the NHL-provided players, often needing to anticipate what the needs will be, and tries to sign players that fill those needs. It will also usually be the AHL general manager who find and signs players from the ECHL to AHL professional tryout contracts when his team is short of players because of injury.
A poor or mediocre AHL general manager may do little more than figure out how many positions he needs to fill and sign the number of players needed without much attention to what the team's shortcomings are. That's why we see, for example,
@orcatown referring to the team needing but not signing muscle and why when the Comets were the Canucks' affiliate we used to see
@Bad Goalie pointing out the failure of RJ to provide a good AHL playmaking center or a sound, knowledgeable but aging on-ice coach type of defenceman pretty much every season.
I can't think of a season since the 2014-15 season when it seemed to me that the AHL players signed to contracts with our AHL affiliate actually filled the team needs other than for the number of players to be provided. Things are improving for our AHL team, but mostly because the NHL team is providing a better calibre of players than was the case a few seasons ago so there isn't as much need for quality fillins on AHL contracts.