Not any more. Apple is so much of a control freak lately that non-app-store apps on Catalina are still required to go through them for "notarization" to be allowed to run on an unmodified OS — and yes that requires the $99 account. For me personally, that's the reason I'm staying on Mojave. That and 32-bit apps.
It isn't just notarization, it is also that notarization requires app hardening which has very strict rules. Shipping an app with 3rd party binaries that supports older versions of macOS is especially tricky to get right.
Also using direct distribution you have to deal more with Gatekeeper.
One particularly fun issue is that if you distribute your app as a zip and a user downloads (to their standard ~/Downloads/ folder) and runs it, then Gatekeeper will use path randomization (aka app translocation), which effectively makes the app look like it is on a read-only volume. Older versions of the sparkle update framework would not show update prompts if on a read-only volume (as what's the point?), and therefore if a user continued to run an app from their downloads folder they would never get updates!
Apple made this change without informing any developers that their users could be left behind for a while. I imagine this security feature prevented users from getting many security fixes.
The way to disable the app translocation is to have a user manually drag the app to their Applications folder, which is why so much software is distributed in DMGs now with the Applications folder symlink.
Now I remember seeing these weird long paths pointing to weird places with the word translocation in them — never really dug into the why. I've also seen apps ask to move themselves to /Applications when launched from ~/Downloads.
Anyway, with all these Gatekeeper changes, it's almost as if Apple doesn't want non-app-store apps at all.
Of course that's their idea, The Mac Store has been a moderate failure, so now they are pushing people into it slowly more and more every release.
As Apple and Microsoft (with their Windows Store) have learned, if there's a real choice between an app store and a standard install, nobody will pick the app store. They cannot promote it naturally, they have to push it through by force.
Apple themselves ships some software, like the non-Mac App Store versions of Xcode, as xips (signed zips), but for some reason decided 3rd party developers cannot use these.
Apples recommendations are in the "Shipping your Signed Code" section of this tech note:
https://developer.apple.com/library/archive/technotes/tn2206...
Apple tries to hide the option, but you can still run non-notarization software on a Mac. The first time you run the application, open in from the right click menu. It'll give you a warning, and if you select OK it'll run. After that you can just run it by double clicking like normal, and it won't warn you.