I see no reason why he will not, although expectations for this season must be tempered by the fact that he is currently the second-team tight end and is in his first on-field season after missing his rookie campaign because of a torn ACL.
In the last 10 seasons, just nine rookie or first-year tight ends have posted at least 500 yards receiving, according to pro-football-reference.com. Only nine have caught at least five touchdown passes in their first NFL seasons, including three in the last two campaigns (Hunter Henry of the Chargers in 2016 and Evan Engram of the Giants and Tampa Bay's O.J. Howard last year).
If Jake Butt finishes with 400 or more yards and five or more touchdowns, then that would make him just the 21st rookie, first- or second-year tight end since 2008 to hit both of those milestones. Such a season would rank among the top 4.0 percent of young tight ends for the last decade, according to pro-football-reference.com.
I think Butt has some great days in front of him. However, maintaining reasonable expectations for him is advisable.
Actually, San Francisco is the Broncos' most common preseason opponent. Denver and the 49ers have met 39 times in the preseason, with the Broncos holding a 22-17 series edge. They even met twice in consecutive preseason weeks one summer -- in 1995, when they played in Tokyo, then dueled again in Denver. (Tokyo was the site of Terrell Davis' thunderous tackle on kickoff coverage that helped him earn his coaches' attention, launching his brilliant career.)
Arizona is the second-most frequent preseason opponent. The Broncos-Cardinals game on Aug. 31 will be their 27th preseason meeting, with the Broncos currently holding a 17-9 edge. Dallas and Indianapolis follow with 15 and 13 appearances, respectively, on the Broncos' all-time preseason docket.
As for how the games are chosen, the league handles scheduling for the first three preseason games. Usually travel and convenience are considered, which is why Dallas, Seattle and Houston have been frequent opponents in recent preseasons. The final preseason week is arranged by teams, and for the Broncos, Arizona has been a frequent and logical foe, since Phoenix is the second-closest NFL market to Denver (the closest, Kansas City, is a divisional foe, which teams try to avoid in preseason play).
The weirdest one, in my opinion, is the one of the piccolo player from Villanova's pep band in tears after the Wildcats' Round of 32 loss to North Carolina State in the 2015 NCAA basketball tournament. Imagine having a moment of emotional vulnerability captured in molded resin for all time. That just seems strange, although I read an article in which she said her parents displayed the bobblehead, so I guess it's all good.
There's an easy answer to your second question: Steve Atwater. I can't find an Atwater bobblehead anywhere. National Bobblehead Museum -- yes, there is such a thing, in Milwaukee -- get on it, please -- and pronto. A bobblehead depicting his hit on Christian Okoye or his successful attempts to get the wave going around Mile High Stadium would become a must-add to any Broncos fan's collection.