When paired with supported 64-bit Creative Cloud versions (like Illustrator 2020/v24 or slightly later), user experiences on Catalina have been mixed but generally stable after initial patches.
(such as version 24.x), as these are known to be compatible with macOS 10.15. on the older version. Key Constraints to Keep in Mind 34-Bit Support: adobe illustrator macos catalina
Prior to Catalina, macOS maintained backward compatibility with 32-bit applications. macOS Mojave (10.14) was the last version to support them. With the release of Catalina, the operating system would simply refuse to launch any application not built with a 64-bit architecture. When paired with supported 64-bit Creative Cloud versions
Adobe Illustrator on macOS Catalina (10.15): Compatibility, Solutions, and Upgrades adobe illustrator macos catalina