yes you can - on an unsupported Mac running beta Mojave - the download button in the App Store redirects to the system settings update panel and downloads the installer.You can't download it from the App Store onto an unsupported Mac. The App Store blocks the download with an error message, i.e., "this version cannot be installed on your computer" or words to that effect.
Has the Patcher been updated to download 14.0.22 yet?
You cannot run the unpatched installer, but create a patched USB stick