I suppose you could do it, but don't.
There are some sites that are claiming that they have firmware 1.5 downgrades you can run on your Sony PSP and have it magically go back from firmware 2.0 to firmware 1.5.
In fact, they're cleverly disguised trojan horses, programs that are actually written to destroy your PSP unit. If you run one of these downgrade applications, it'll actually remove some key files from your PSP and render it inoperable, which would definitely ruin your day.
As far as I have read, there's also no way to send your PSP to Sony or otherwise have someone clone their OS onto your system as a recovery mechanism (though theoretically you should be able to accomplish this task with some simple programming). If you run this trojan, known in antivirus circles as Trojan.PSPBrick, you'll have a dead, throw it away, nothing you can do to fix it Sony PSP unit.