If my head unit is 4x50w and my speakers are rated 35w input do I NEED an amp?
No you do not need an amp. When you turn an amplifier up to max, they generally send a distorted signal to the speakers, which is how most people blow them, therefore: You should always over power speakers so the amp doesn't send a distorted signal to the speakers.
I have a 75w RMS per channel amp running 40w (i think) speakers. If you wanted to deafen yourself you could turn it up to max and the speakers would not blow. If it was the other way around (low wattage amp, higher wattage speakers) they would probably blow. It's the same for home/pa amp/speakers too.