No, it's not. It means if you make your case yourself instead of waiting to be noticed, you are more likely to be rewarded.

That's true regardless if the wheel squeaks or not. <insert won't get promoted to wheel drive pun here>

I thought oil was money in this metaphor.

I think you're gravely mistaken about that. I have absolutely heard people quoting this to justify demands of rewards, whether monetary or status; an even pithier version is 'if you don't ask, you don't get.'

I once worked with someone who got both of us a pay rise by vocally complaining to a senior manager.

He specifically used the "Squeaky wheel gets the oil" metaphor to describe what he'd done and why it worked.

The "oil" is money.