Absolutely not. This is one of the worst ideas about how to fix the government I've ever heard. If the Fed is doing something they aren't "supposed" to be doing, exposing it will only bring the problem to light and shatter confidence. Economics is all (well not all, but a whole lot of it) about confidence, whether it be in future growth or the value of our currency. Intentionally taking a risk like this, with little or no apparent upside value, is a terrible idea.
And if all of that doesn't scare you, the very thought of the Fed being run by Congress ought to.
I'm kind of on the fence on this one... but what if the Fed is actually doing something that will hurt the economy in the long run? Say then, maybe, those wrongdoings were to be discovered later and confidence is shattered, then? I get the whole 'ignorance is bliss' idea, but letting such a powerful arm of the government like the Fed go totally unchecked just sounds foolish to me.