By itself, the phrase "see for yourself" means to look at something with one's own eyes.
By itself, the phrase "see yourself" is a phrase in the imperative mood; that is, it is a command telling someone to look at themselves.
In the example that you gave, you could say "see yourself" and the person will know that you are non telling them to look at themselves, rather you are telling them to look at what was specified.
However, they will only know that because of context, and not because "see yourself" can have the same meaning as "see for yourself". It doesn't. Just like how I can understand someone even if they break some grammer rules, so to can a person understand what is actually being said in that sentence despite its incorrectness.
Long story short, it is not correct to drop the 'for'.