USB ports can supply up to 500mA per port for powered ports, and 100mA per port for unpowered.
Also, the hubs usually say they draw 100mA of power, that is why you usually see four port unpowered hubs (100mA for the hub, and 100mA x 4 ports = 500mA which the powered port can supply).
Not all devices require 100mA, for example, I had a mouse that take 20mA. I assume that as long as the power the 7 port hub is less than 500mA, you will be fine. If it is more, Windows is smart enough not to power on the devices to protect the USB port.
External hard drives are usually powered by themselves, so I assume their power requirements are low. If you are in Windows you can see the power requirements in the Device Manager, under Universal Serial Bus controllers. There will be a list of all the hubs. Looking at the properties of the hub there is a Power tab. It will list all the devices attached to the hub and their power requirements. Many devices will list 100mA because that is the maximum an unpowered hub will supply.
I hope this helps explain why the devices may still work, and put your mind at ease that the computer is probably smart enough to protect itself.
(The only thing about using external drives is some drive can be self-powered or bus powered. Some of those drives will spin slower if they are bus powered, and will spin faster when self powered because they can pull more current. I've only seen this once so I don't know how common this is, the external drive had a laptop drive inside. This may be something to consider if you have drives of that type.)
A voltage spike from the hub could damage or destroy any USB device connected directly to it. This is true for both self-powered and bus-powered devices, because the spike may occur not only in the power connection but also in the data connection itself.
That being said, this is rather unlikely. Less unlikely are brownouts due to insufficient power, which could result in data corruption or other errors.
Best Answer
It's safe. I'd give you a more detailed answer, but I don't know what hazard you're imagining, so it's hard to know what else to say.