First of all, VBUS (5V) coming from the Host is required for the Hub to detect the connect/disconnect status for non-embedded Hubs.
It is possible to obtain 3.3V and 1.2V from VBUS, but it can power HX3 IC but cannot provide sufficient power to the downstream connected devices. So, it is recommended to use self powered Mode for USB3.0 Hubs.
Please refer "Power Consumption" section in the HX3 datasheet at http://www.cypress.com/file/141031/download
which lists the power consumption of the HX3 in different cases.
And for your reference, USB3.0 Host can provide only 900mA@5V.