Is this possible, or even desirable?
My work won’t allow Dropbox or any other cloud services. They use Google Drive exclusively, but apparently Scrivener is unreliable with Google Drive.
What are some potential workarounds? Or am I stuck with copying and pasting by using Google Docs as a go between?
Check out this method (works also with Google, or an USB thumb drive): Alternative Method of Keeping Projects Synced / Cloud Syncing / Knowledge Base - Literature and Latte Support
A Scrivener project is just a folder. You can use any file transfer mechanism you like.
Just be aware that what you’re doing is copying a folder. That is, keeping track of which version is which is up to you. Especially with more than two devices, you’ll want to have a very clear protocol for managing your updates.
To add to @November_Sierra’s post, there’s a little bit of a wrinkle with iOS devices, in that you need to use Apple’s File Sharing tools. But the fundamental idea is the same.
Minor point. It’s not that Scrivener is unreliable with Google Drive, it’s that Google Drive has been ‘unreliable’ (screwing projects) with Scrivener. There’s some suggestions the latest GD update works, provided you ensure files are available offline, or whatever their description of that is (some cloud services call their online only mode as ‘optimise storage’ or similar.)
I’m normally a risk taker with non-essential data but haven’t bothered to give this a try yet with the current Google Drive. Apparently with the old version it could work fine for months then one day - wham!
Any update from the L&L team on this?
One of the main problems encountered now and then is that—either of its own volition or some user-initiated command done without fully considering the consequences—Drive would convert all of Scrivener’s RTF files to .gdoc files, which aren’t even text files, but pointers to a URL where the Google Docs file is online. That result is, naturally, catastrophic if your backups aren’t good. But I believe there are other issues as well that have lead to it being something we recommend avoiding.
At any rate, I second the advice given by November_Sierra. This is the method I use even when I can use sync, mainly because it’s all around a safer way of working, and once you get into the flow of using it that way, it’s barely any overhead to think of. It also encourages better backup awareness and use. While most people might have a panic when they mess up, not knowing how to recover, fumbling around for old files—you’ll know exactly where to go to get Tuesday’s draft that you accidentally pasted a website over last Wednesday.
I wrote a bit on why this method is so safe in this post, as well as elaborated a bit on my workflow. Some people get a bit nervous about the concept of having to remember to copy the latest version of your project down from the sync folder when switching devices. In short, that’s a teething problem that you get used to very quickly. Secondly, it’s not even a risk, as I go into in depth in that post. “Messing up”, and recovery from that, is identical to the procedure you would use when collaborating with one or more Scrivener users. You’re just… collaborating with your past self’s mistake. 
The end result is seamlessly merging the two copies back together again in a few seconds, and getting back to work.
I encourage trying it on purpose, then you can see how it works, and you’ll know what to do if it happens.
Thank you all. It’s very encouraging to hear that there’s an alternative method that is even safer. The only resistance I have is that I FINALLY got used to remembering to close out all my projects switching between devices and using Dropbox, and now I need to learn a new thing.
I should have been more careful with my wording in my original post. I did not mean to cast aspersions on Scrivener w/r/t the Google Drive issue. 
Well one good thing about that habit being formed is that, by default anyway, closing the project is what triggers a backup, which is the central component that makes this way of working semi-automatic. There are other ways to trigger a backup as well that do not require closing, such as one of my favourites, back up on manual save, but I still leave “on close” enabled because that’s a really good setting.
The beauty of “syncing” via backups (especially zipped ones) is that it removes all uncertainty if something got damaged or missing in the transfer process, somewhere deep in the belly of a project. Which may consist of thousands of files. It’s possible to corrupt an archive, but it’s impossible to not be aware of it the moment you try to unpack it.