My local hobby shop has a bin for sprues. It was ABS last I checked (like 20 years ago) so see what your local recycling center accepts.
Some guy on YouTube is making/made a Tau Manta (giant 1 m wingspan flyer) out of sprues and I think acetone.
I was thinking about using it for hobby stuff, but I got told sprue goo is a waste of time. I could use it for pipes for terrain or whatever, but I don’t really have plans to make any.
It's handy to make a thin mix for gap filling, but I don't think I'd try to sculpt with it
Yeah mix in leftover bits into some Tamiya extra thin cement and you will have the ability to make absolutely seamless joints. Very handy when gluing body parts together where skin is exposed and you want there to be zero gaps.
Example using my trolls (specifically their tummies):
What it looks like when you don't use sprue goo to fill in the gaps:
Like JFC look at that joint near the love handles!
I love your trolls! Very swampy 
Some guy on YouTube is making/made a Tau Manta (giant 1 m wingspan flyer) out of sprues and I think acetone.
MiniatureHobbyist! He finished the Manta a while ago and has been doing more painting, but he's been back to doing sprue stuff these past few weeks.
https://www.youtube.com/@MiniatureHobbyist/videos
The hard part about using goo is all the air bubbles. It's fine if you're doing something like Nurgle or terrain, but the bubbles get really bad if you're trying to make anything like Eldar vehicles and need sharp details.
I think the plastic is polystyrene, which isn't typically recyclable at a municipal level.
Correct. Polystyrene is why it dissolves in acetone and plastic cement.
Short answer no
Long answer you can but ultimately no
Most places don't have the recycling facilities for styrene, so if you put it in your general recycling, it will just get moved to the trash. Your best bet is to use sprues to make terrain and vehicles with, like this:
Orc Wagon:
WW2 entrenchment and barb wire fence:
I shaved some sprues into round "logs" and put the shavings into a jar of Tamiya plastic cement to make some sprue glue. This gets used for gap filling and making seamless transitions. The logs I used to make the wagon axles, parts of the wagon's overall structure, and livestock padding. Other logs were cut into various lengths to make posts for the barb wire or logs to reinforce the trench walls. What's especially nice about using them to make the trench is they fuse together to make really sturdy terrain.
I forgot to mention, you can also cut sprues down into rock shapes or straight-up use a blender to grind them into pieces.
...or make new models (spruecrons are especially popular):
Wanna talk about your hobbies or post about them? Here's your spot! From mini painting to cross stitching to crocheting.