This, as you might expect, is music to Conner's ears.
"Until it happens, you're waiting and waiting, and a little bit uncertain if it will fall that way," Conner said. "But as soon as those deals become official … you start thinking it's going to be an exciting year for the scouting department.
"It's always fun to have extra picks."
Here's how it breaks down for San Diego:
The Padres will have their own first-round selection (No. 8 overall, which is a protected pick), two compensatory picks after the first round for losing Kennedy and Justin Upton -- who signed with the Tigers on Wednesday -- a second-round pick, a competitive balance pick and then their third-round selection.
So what kind of class will comprise the 2016 Draft? Jim Callis of MLBPipeline says this particular Draft doesn't rate as exceptional.
"Like most of the Drafts this decade, with the exception of 2011, the 2016 crop looks pretty ordinary," Callis said. "That said, there's talent in every Draft, and the Padres will be better than most clubs to capitalize thanks to their extra picks.
"There's no clear No. 1 overall choice, and the pitchers stand out more than the hitters toward the top. The up-the-middle players are lacking -- not a lot of catchers or shortstops, and many of the best outfielders may wind up on the corners."
The team will tackle this Draft with a revamped amateur scouting department -- as eight scouts have left since last season, with 10 new hires on board.
"There are some great people who are no longer with us, but we feel that we've added some great people," Conner said. "We have some talented guys who are going to be impact evaluators and talented scouts for us."
Such a windfall of early Draft picks isn't unusual for the Padres, who had six of the first 70 picks in 2012. The most picks that the team has had in recent years was eight in the first 87 picks in 2007.
The sheer number of picks is nice, of course. But the Draft is really about what a team does with them.
Take the Padres' 2007 Draft. Of those eight picks, only left-handed pitcher Cory Luebke made the big leagues with the team. Infielder Eric Sogard (traded to the A's) has a 3.7 WAR, though he never played with San Diego. Indians pitcher Corey Kluber was taken in the fourth round that year, but his 12.4 WAR have all come in Cleveland, as he was traded away as a Minor Leaguer.
The Draft surely hasn't been kind to the Padres, who largely have failed to keep up with teams in terms of graduating impact players to the big leagues.
Since 2000, the only two players with a WAR greater than 10.0 accumulated with San Diego are Chase Headley (22.3) and Will Venable (13.4). Both players are no longer a part of the organization.
This would at least partly -- or largely, depending on your vantage point -- be the reason why the Padres haven't reached the playoffs since 2006.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.