No, you will get the full amount. However, you will begin to loose resources due to corruption if you are above your total capacity. It will also shut down production on any resource you are over capacity on. Below are what contribute to the storage capacity.
Base capacity: 100k
Storage / Cache: (What you build up to.)
Fleet hold: The capacity of your fleet to hold and carry resources.
Check on the raw material tab ( 3rd one or click on bar at top of page that tells you current amounts.) for what these values actually are. This will also tell you how much over you are, the rate you are loosing material, your current production / costs and many other useful details.