No, actually not. The time to amp the signal is before the splits. Every time you split the signal, the signal level and the noise floor level get closer. After so many splits (depends somewhat on what the signal level and the S/N levels were before the split), amplifying the signal just amplifies the noise right along with it .. no real performance gain is achieved.
It's like this: every time you do a two-way split, you half the signal, and lose a little of the signal from each split because of the losses in the (passive) splitting device. If you split again with a passive device, you're down to below 1/4th of the original signal level (~7-8 db down). This is about as far as you can split a common signal without seriously affecting the quality.
Unless you have a good Field Strength Meter, there's no way to really tell what level you're starting out with.
You CAN have too much signal. A signal that's too hot looks worse then a weak signal in many cases.
There are (as usual), many variables that modify the above statements but, generally speaking, that's it in a nutshell.
Good Luck
Scott