No. macOS Catalina is the first version that only supports 64-bit applications. Check your apps before upgrading using System Information > Software > Applications, and look for the "64-bit (Intel)" column.
Only download from official Apple sources or use verified tools like gibMacOS that download directly from Apple's servers. Third-party websites may distribute modified or malicious files. Always verify the hash values after downloading.
Even with a legitimate DMG file, you may encounter installation issues. Here are solutions to the most common problems.
shasum /Applications/Install\ macOS\ Catalina.app/Contents/SharedSupport/SharedSupport.dmg