No. WinRAR is a file archiver (`.rar`, `.zip`, `.7z`). It is **not required** to install games on a PSP. You only need it if your downloaded game files are *packed inside a `.rar` archive* — and even then, 7-Zip (free, open-source) or Windows built-in ZIP support handles it fine.
Downloading ISOs for games you do not own is piracy. Dumping your own UMDs to ISO (using UMD Dumper on CFW) is legal archival in many jurisdictions.