Powering a usb hub using a different source
Will this allow the pc to send data to the hub?


Not if you connect the tablet...

Reason behind this: The hub still identifies itself as being bus-powered, and thus the charging current of the tablet -reported via USB- would (probably) be above the (100/400mA) limit for bus-powered USB hubs. In this case the host os will complain with an error message and not allow you to transfer data.

Alternatively the tablet might use a rather low current over USB in data mode, that usually discharges the battery (at least with the screen turned on).

It is not possible to fast charge a tablet and use USB in data mode, because the data lines are used to recognize the fast charging capable USB power source.

USB-C finally changed that - but both tablet and hub/PC must use this port type.