On Windows 10, I have 64-bit Opera installed to "C:\Program Files\Opera" and 32-bit Opera installed to "C:\Program Files (x86)\Opera". Both work fine (only run one at a time) and I can confirm in the task manager that they're the proper bit process. I can also confirm that they have the correct user agent strings.

I used the offline installer for the 32-bit version of Opera from https://ftp.opera.com/ftp/pub/opera/desktop/65.0.3467.48/win/ (the one that doesn't have x64 in the filename).

So, all is good. But, I didn't test if an auotupdate of the 32-bit version of Opera gets converted to a 64-bit version. It shouldn't though. Now, the net installer (which fetches the installation files itself) should always grab the 64-bit files on 64-bit Windows, so you'll want to avoid that if you really want the 32-bit version.