No. PSP UMDs (Universal Media Discs) are read-only optical media. Data is permanently pressed during manufacturing. They cannot be burned, rewritten, or modified by any consumer device.
No consumer laser can modulate the UMD recording layer. Any attempt will physically damage the disc, rendering it unreadable.
Use a large Memory Stick (16/32GB) + CFW for your game library. Keep UMDs as collectibles/archives.