I am about to upgrade my host operating system to macOS Catalina. According to release notes from Apple, with the release of macOS Catalina, 32-bit application support is no longer available. Will I be able to run my 32-bit applications in a virtual machine created with Parallels Desktop?
macOS Catalina does indeed drop support for macOS 32-bit applications. At the same time, Parallels Desktop is a 64-bit application so it is absolutely compatible to work under macOS Catalina.
In regards to running Windows 32-bit applications in a Windows virtual machine after upgrading to macOS Catalina, please be informed that Windows applications running in Parallels Desktop virtual machines are not subject to limitations of macOS Catalina as they are running in a virtualized environment. This means that you can proceed further with the macOS upgrade and create a new Windows virtual machine for these needs or continue using the Windows virtual machine you have already had. However, as per Apple's instructions, we recommend you to make a full backup of your Mac before performing the upgrade.