It's not worth it at all
Okay I'm out of my laziness, and I guess I'll just answer this lol. There're a lot of reasons because of which TrickChoice + Encore won't be a nice idea, and I'll try to list all of them out here.
1. Why use Encore when you've already tricked a Choice item lol
I still don't get why you'd want to use both Trick (with a choice item) and Encore on an opponent when both of them do the exact same thing...
If you're holding a choice item and Trick it onto your opponent, they would get locked into the move they're about to use; that is exactly what Encore does - it locks the opponent into the move they last used. Why use both? You're just wasting a moveslot imo.
commented 1 hour ago by Aaaaaaaaa
That pretty much summarises this point. A Choice item locks the holder so that it can use only one move, and Encore does the same but for three turns -- so why would you use Encore on something which is already move-locked? Granted, if your opponent is faster than you and you trick your item after they move, you will have a chance to use Encore, but if it's faster than you it will be faster after tricking a Choice item, too, so it won't be very nice as they'll be locked into a move of their choice.
2. 3A/2A + Choice Item is, usually, better
With a Choice item, you either want to hit hard (Band, Specs) or revenge kill a certain foe(s) (Scarf), or just have it for TrickChoice (usually Scarf). In all of these scenarios, you'll usually be going with 3 or 2 attacks + the Choice item, which really won't leave space for Encore.
Let's take an example of Gengar, which gets both Trick and Encore. For sometime, Scarf Gengar was pretty common in SS OU. It used to run Trick / Shadow Ball / Sludge Wave / filler, usually Focus Blast. Now why will it run Encore with a Choice item, even if you have Trick? TrickChoice cripples its common checks and counters in Landorus-Therian, Chansey etc. easily, Encore would be a waste of a moveslot. You'll loose on important coverage in Focus Blast, which would make checking the Gengar very much easier.
2A + Choice item is also common, as some Choiced Pokémon run Trick + say, Aromatherapy + two attacking moves, like Calyrex-Shadow in SS Ubers and AG. Aromatherapy, as an example, is far far better of a move than Encore, as it has more utility than the latter.
1A + Choice item is far less common, but there are a few examples. Usually, Scarf Xerneas in SM Ubers and AG runs Moonblast / Thunder Wave / Aromatherapy / Defog. The latter three moves are ran because of the number of switches it forces, making it easier for it to, say, Defog or use Aromatherapy.
None of the examples I mentioned above run Encore + a Choice item. It's a pretty vague combo and it won't really work very nicely.
3. The opponent can switch
The opponent can just switch after you've Tricked a Choice item to them. As you, usually, won't have a trapping ability/move activated, this point is one of massive concern as switching can render all your hardwork in predicting and tricking useless. After they come back in, they can choose a move of their choice and be locked into it -- your Encore won't be able to do anything, too. Also, #1 + #3 actually proves why Trick + Encore + Choice item isn't a good combo.
These are all the points I could think of. If I have missed any, feel free to comment. Hope it helped!