Apple - Does macOS Mojave (10.14) support 32 - bit Apps?

Yes

As of macOS Mojave (10.14) beta 9, macOS Mojave DOES support 32 - bit applications. When opening these applications, you will see a dialog box with a similar message from High Sierra (see below) telling you that "This app will not work with future versions of macOS" but after clicking "Ok" the application will open.

For example, I attempted to open an old version of Firefox (3.16.14 from 2010) that is 32 - bit and got this message

After pressing "Ok" it opened

Sorry about Spanish, only version I could find.

It's confirmed on the State of the Union that the final version of macOS 10.14 Mojave support 32-bit and it will be the last macOS that support it.

From https://www.macstories.net/news/macos-mojave-a-roundup-of-all-the-little-things/

The Final Version to Support 32-Bit Apps. During the State of the Union presentation, Apple confirmed that Mojave will be the last version of macOS to support 32-bit apps. When a user tries to open a 32-bit app, Mojave currently displays a one-time warning that the app will not work in future versions of macOS.

Or watch the Platforms State of the Union video at https://developer.apple.com/videos/play/wwdc2018/102/