I would say no, but this of course depends on your definition of overloaded. Bitcoin network is overloaded with 220 thousand transactions waiting to be confirmed, but if I were willing to pay the right fees, I could still always get my transaction confirmed within an hour. And so the same with ETH.
These are all temporary demand spikes, ETH because of their cryptokitties game, BTC because of huge demand from BTC buyers (or spam, if you follow the theory from those trying to take Bitcoin down and promote other alts like Bitcoin Cash).
So, raise gas and GWEI And keep on keeping on. Sure. I wonder though at the ability of one product to have this much impact on the overall service. Is there a correlation to the number and power of miners available as well??