But when would that be?
First, understand that, despite the quality of picks that had ESPN.com's Keith Law (subscription required) tabbing the Red Sox as one of four teams that got the best value on Day 1 of the draft, the first two picks were used on high school players.
These players are generally anywhere from 17-19 years of age and tend to need at least two additional years of "seasoning" in the minor leagues that more advanced, college-level hitters wouldn't need.
So it will take some time before Red Sox fans can cheer on shortstop Michael Chavis or pitcher Michael Kopech, but that time should come.
That time will be even earlier for Sam Travis, a first baseman selected in the second round of the draft. He played at Indiana University, so he's older and should advance quicker through the Red Sox system.
Round 1, Pick No. 26: Michael Chavis, SS, Sprayberry (Georgia) High School
Chavis has excellent bat speed and has sneaky power for someone who doesn't appear to be a thumper. The 18-year-old's raw power is as good as anybody's, according to an evaluator who spoke to WEEI's Alex Speier. With those kind of rave reviews, Chavis should move steadily, if not somewhat quickly, through the system.
He may not stay at shortstop, as the industry-wide consensus is that he likely ends up at third base or possibly second base. Clint Longenecker of Baseball America believes Chavis will land at third base and could even potentially catch.
Mike Andrews, writing for SoxProspects.com (via ESPNBoston.com), believes Chavis is about four years away from his major league debut. That's a solid guess, as that would place Chavis' arrival in Boston during his age-22 season, although he would turn 23 by year's end.
If Chavis does end up behind the plate, that would probably delay the first-rounder's arrival. Making a seamless move to behind the plate this late in the game would delay Chavis' defensive readiness, as he would need to learn all the nuances of being a backstop.
Further, the pressures and physicality demanded of catchers tend to affect the quality of offense. Depressed offensive numbers would also slow his progression through the system.
All told, 2018 as a major league arrival year looks solid. He would most likely be a September callup during that year to prepare him for full-season play in 2019. If he does indeed move behind the plate and become a catcher, his arrival date would probably be pushed back a year to a debut season of 2019 for full-time play in 2020.
Round 1, Pick No. 33: Michael Kopech, RHP, Mount Pleasant (Texas) High School
The Red Sox drafted a high school player in the first round for the second year in a row. Last season, Boston used its No. 7 overall pick on left-hander Trey Ball.
Kopech has arm strength "that would stand out against any crop," as Longenecker writes.
High praise. But it doesn't stop there.
An evaluator tells Speier that "I don't know that I've ever scouted someone who's had this kind of arm strength. ... It's a special, elite type of arm."
That type of arm strength plays up Kopech's fastball, but as Speier notes, it also, in a sense, sets the 18-year-old back because he didn't have to rely on secondary pitches in high school play to blow away hitters. That alone sets his projection date far into the future, and he may not pitch much more this season.
Andrews notes that his high workload in high school, which totaled 64 innings before continuing to pitch at showcases in preparation for the draft, could mean his professional innings are limited once he signs with Boston.
Taking all this into consideration, it's unlikely we see Kopech before the 2019 season, and he probably doesn't play a significant role until 2020. Given Kopech would turn 23 during the 2019 season, the lengthy wait isn't a knock on Kopech—it just takes time to develop high schoolers.
Round 2, Pick No. 67: Sam Travis, 1B, Indiana University
Travis should reach the major leagues a lot faster than Chavis or Kopech.
The 20-year-old was one of Law's "favorite hitters in the college crop." That came on the strength of an ability to make contact with the ball and can drive the ball out of the park, as Andrews writes.
Andrews sees Travis as a potential starter in the major leagues but not one who could reach an All-Star Game, unless Travis takes a big step forward. Still, the power that Travis brings to the table is intriguing. The first baseman may also be able to make the move to left field, Law adds. Essentially, Travis could be a younger, cheaper version of Mike Carp in short order.
Red Sox scouting director Amiel Sawdaye is high on Travis, per Speier. As Speier tweeted, Sawdaye said of Travis that "the hit tool is very advanced. Excellent recognition skills. Aggressive but with really good plate discipline."
Andrews believes that Travis could end up at Class A Greenville before the end of the season, which would put Double-A Portland in Travis' sights for 2015. Once he hits Double-A, the major leagues should not be too far off.
Assuming Travis does reach Greenville in 2014, makes his Double-A debut in 2015 and spends most of the year at that level, he could be in Boston by 2016, although he would be unlikely to play a significant role until 2017.
RELATED: See Bleacher Report's Ben Carsley's take on where the draft picks would rank in Boston's current system.