Not at the same time.
Does your Di Gold have the vst plug-ins?
If so you could record vocals with the UX1 and the use the DI Gold to access your plug-in tones (assuming it has a license for the plug-ins).
I'm pretty sure the DI Gold came with all the packs as Factory add-ons, if that is the case, you can not authorize them to another device.
You can tell by running the License Manager. If the Model Packs show as italicized then they are factory add-ons.