Not right now, anyway.
It's way too early in Gregory's career. He's about 245 pounds now, up from 238 after last month's draft. But the 6-foot-4 rookie's metabolism is so efficient, his goal weight remains a moving target.
We are talking about a guy who said he lost 1 1/2 pounds in about 30 minutes in the rookie minicamp.
"We don't want to be overly overly concerned about that," Garrett said of Gregory's weight. "One of things you do notice is he's an explosive player, a physical player, despite what the number might be on the scale."
Realistically, Gregory will need an entire offseason to put on and maintain the kind of weight the Cowboys want him to carry.
In the meantime, defensive coordinator Rod Marinelli's job is to give Gregory a crash course on rushing the passer.
Marinelli, who owns a Ph.D. in football technique, has Gregory studying game tapes of former sack masters Simeon Rice and Jason Taylor. Each player had a linear frame similar to that of Gregory, and each finished his career with more than 100 sacks.
At 6-foot-5, 268 pounds, Rice had double-digit sacks in eight of his 13 seasons. Taylor, 6-foot-6, 255 pounds, had six seasons with at least 10 sacks in his 15-year career.
"We're just looking at guys who kind of fit his movement, just to see things," Marinelli said. "You don't try to make a player that guy, but both of those guys rushed with great instincts.
"The awareness, the feel. You try to give guys a look at what it is and why they're so good."
The Cowboys finished the 2014 season with just 28 sacks, which ranked 28th in the league. Defensive end Jeremy Mincey led the Cowboys with six sacks.
That's not nearly good enough for a team that now believes it is in line to compete for a title. More pressure from the Dallas defense means opposing quarterbacks operating under duress, which usually leads to turnovers and wins.
DeMarcus Lawrence, a second-round pick last season, should be considerably better in 2015. And it will take some time, but sooner or later defensive end Greg Hardy should be a difference-maker, depending on how long his impending suspension lasts.
There's no doubt Gregory will also get an opportunity to be an impact player this season.
That doesn't mean you should expect him to get double-digit sacks, but if he's healthy and plays the entire season, Gregory should be able to impact the quarterback. Thirty-two defensive ends have been drafted in the second round since 2004; during their rookie seasons, none had more than Carlos Dunlap's 9 1/2 sacks for the Cincinnati Bengals.
Most have been average as rookies and increased their sack total by four or five during their second season.
Gregory has long arms to keep offensive tackles off him, and his first-step quickness gives him a chance to be an elite pass-rusher.
The tackles in today's NFL are usually nimble 300-pounders. Good technique is a necessity for an undersized dude like Gregory to survive and thrive.
The first three steps, Marinelli said, is where a play often is won or lost for a defensive end.
"Their feet, their takeoff and their pad level is so important, and that's the hardest thing to get," Marinelli said. "It wears you out every down. It's hard to be exact, because you're going full speed.
"It's not just running wild. The skill level you're trying to teach is unbelievable. He can bend. But he's got to come off the ball better. He's not coming off the ball quick yet."
At the same time, Marinelli doesn't want Gregory thinking about how fast he reacts to the snap. The defensive coordinator wants it to be intuitive, something that only happens with time.
Gregory, assigned jersey No. 94, which belonged to Hall of Fame pass-rusher Charles Haley, said he is doing his homework and focusing only on improving daily.
"I've watched a lot of tape of those guys, and I'm trying to learn some of their moves," he said.
"Simeon has a really nice move that I tried in practice today, and that's what I'm trying to do."
For now, pass-rushing moves take precedence over gaining weight.