I decided to look at inexperienced QBs and how their TEs perform. I looked at QBs with three or fewer years in the NFL, who were in their first year as a starter (>300 attempts). Since the year 2000, those are:
2005:
Eli Manning
Kyle Orton
Chris Simms
2004:
Kyle Boller
Carson Palmer
Josh McCown
Billy Volek
2003:
Marc Bulger
Quincy Carter
Byron Leftwich
Patrick Ramsey
2002:
Drew Brees
David Carr
Joey Harrington
Michael Vick
Chad Pennington
2001:
Chris Weinke
Tom Brady
Matt Hasselbeck
2000:
Donovan McNabb
Daunte Culpepper
Shaun King
The best TEs produced by this group were:
1-10 (4):
2005 Shockey (#2)
2002 Billy Miller (#7)
2002 Alge Crumpler (#8)
2000 Chad Lewis (#4)
11-20 (7):
2005 Alex Smith (#20)
2004 Freddie Jones (#17)
2002 Stephen Alexander (#15)
2002 Mikhael Ricks (#18)
2002 Anthony Becht (#16)
2001 Wesley Walls (#12)
2000 Dave Moore (#19)
21+ (11):
2005 Desmond Clark (#30)
2004 Todd Heap (#24)
2004 Matt Schoebl (#28)
2004 Ben Troupe (#30)
2003 Brandon Manumaleuna (#28)
2003 Jason Witten (#23)
2003 Kyle Brady (#30)
2003 Zeron Flemister (#66)
2001 Jermaine Wiggins (#24)
2001 Christian Fauria (#38)
2000 Johnny McWilliams (#26)
The trend here is obvious; on teams with first-year starting QBs, TEs did very poorly. Out of 22, only four produced above the baseline, and only two produced more than 16 points of VBD value vs. the #12 starter. In addition, for almost every TE except 2005 Shockey, this performance represented a down year; better performances were had by the TE before the studied year, after it, or both.
Here are the rankings of the QBs for the TEs who finished above the baseline:
2005 E.Manning: #4
2002 Vick: #3
2002 Carr: #24
2000 McNabb: #5
In three of the four cases where a TE being thrown to by a first-year QB finished above the baseline, the QB finished top-5 in fantasy points. That is, the TEs who performed well from this set benefitted from an overall passing game that was unusually effective, considering that they had a first-year starter at QB.
What does all this mean? Among other things, it clearly shows that first-year staters do not, in general, throw to their TE preferentially. It's already known that teams with first-year starters tend to have poor passing games, and this shows that the TE position is affected as much as, or even more than, other receiving positions. (Eyeballing this list of QBs, it looks like it produced a lot more top WRs than TEs).
There are a number of quality TEs on this list, although Shockey, who had the best season of this group, is perhaps the closest analog to Gates. However, there are differences there, notably that Manning started eight games the year before (197 attempts), and that he threw 557 passes (#3 in the league) in the season in question. Rivers has a total of 30 NFL attempts, all in meaningless games, and it is extremely unlikely that Schottenheimer will have him in the top 10 in pass attempts. In 20 years as a coach, Schottenheimer's teams have been in the top 10 in pass attempts only three times, and never in the top 5. Rivers, having no real game experience, will not get the opportunity to chuck it 550+ times under Martyball.
Gates is extremely talented, but if you project a significant drop in passing production for the Chargers (as I do), you have to project a significant drop in his receiving numbers. I think he will still be in the top 5, probably in the top 3 TEs, but will not be worth the premium that is currently being paid for him in drafts this year.
65 receptions, 780 yards, 7 TD. Good for TE#3.