Yes you can some viruses have been specificaly written to format you PSP and totally make it useless.
has an article about this.
A new Trojan horse claims to help make PlayStation Portable run homegrown software, but instead the malicious code turns Sony's game player into a useless "brick."
The malicious program, which Symantec has labeled "Trojan.PSPBrick," is aimed at a crowd of "modders," or people who seek to hack the portable device so that it can run custom code and official game cartridges.
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