Exeggutor does have use in the sun, though I'm not sure how useful  Harvest is. I've seen it used on something like a Lum Harvest set with  Rest, or just being annoying with Sitrus Berry. I'll do some theorying  and testing, but for right now, I'd say Exeggutor is legit. Highest SpA  for a Chlorophyller too, I do believe.
		
		
	 
DISCLAIMER: 
I'M REALLY TIRED
LumRest allows for not only reliably full recovery (as there is literally no time for Knock Off in this metagame), but it also allows Exeggutor to become a team's reliable status absorber. While Celebi has Natural Cure to invalidate the permanence of status, it can still be forced out by sleep, or aggravated by paralysis. Meanwhile, Exeggutor can easily shake them off and stay in the fray, while also having instant, 100% recovery. It also, unlike Celebi, gets access to both Stun Spore and Sleep Powder.
Notable moves include Ingrain, Synthesis/Moonlight, Hidden Power, Giga Drain, Grass Knot, dual screens, Wood Hammer, Leaf Storm, Swords Dance, Zen Headbutt, Low Kick, Seed Bomb, Substitute, Psyshock, and Trick Room.
I haven't used him, but I'm brainstorming...
[SET]
name: Status + Absorber
move 1: Sleep Powder
move 2: Psychic / Psyshock / Stun Spore
move 3: Giga Drain / Wood Hammer
move 4: Hidden Power Fire /  Rest
item: Lum Berry
ability: Harvest
nature: Modest / Rash
evs: 252 HP / 252 SpA / 4 Spe
Self-explanatory. Rash if you want to use Wood Hammer or something. Hidden Power Fire for coverage or Rest for recovery. Can switch in on status moves easily. An alternate EV spread/nature is likely better.
[SET]
name: Physical Sweeper
move 1: Swords Dance
move 2: Sleep Powder
move 3: Giga Drain / Zen Headbutt
move 4: Low Kick / Hidden Power Fire
item: Choice Band / Life Orb
ability: Chlorophyll
nature: Adamant
evs: 4 HP / 252 Atk / 252 Spe
Speaks for itself as an obligatory Chlorophyll set. Competes terribly with Shiftry.
[SET]
name: Trick Room Sleep Supporter
move 1: Trick Room
move 2: Sleep Powder
move 3: Giga Drain
move 4: Hidden Power Fire / Rest
item: Lum Berry
ability: Harvest
nature: Quiet
evs: 252 HP / 252 SpA / 4 Def
Serves the role of a Trick Room user, status spreader, and status absorber. It also has the power to do some damage of its own with Giga Drain and Hidden Power. Defensive spread is probably best, but I suck at coming up with them.
[SET]
name: Screen Support
move 1: Sleep Powder
move 2: Reflect
move 3: Light Screen
move 4: Rest / Leech Seed / Giga Drain / Leaf Storm
item: Lum Berry / Light Clay
ability: Harvest / Chlorophyll
nature: Timid
evs: 252 HP / 4 Def / 252 Spe
Exeggutor is the only Pokémon (besides Smeargle) with access to Sleep Powder AND dual screens. While it sacrifices Light Clay, Exeggutor also has access to 100% recovery with Harvest, which can allow it to easily last through the battle to provide screen support and absorb status. If using a Drought team, Chlorophyll is probably more useful, as 458 Speed is amazing (other Speed EVs / nature can be used, I guess, depending on what you need to outspeed... too lazy and tired, right now, since it's pretty much morning now).
Not sure what could be done with a Custap Berry, once it's released... Maybe a sweeping set. Actually, Trick Room + Swords Dance would be pretty much just as good and more reliable, but Custap could free room for Sleep Powder, I guess... 
I'm really damned tired. Don't blame me for idiot ideas. Actually, blame me, because I really should be sleeping right now.
-Zane
P.S. I hate to be an eager McBeaver but... If deemed viable, DIBS. c: