Obtained Umbra early (spoilers)

[Maqabir]

After obtaining Excalibur Umbra I made a new loadout slot for it before exiting my arsenal. 

Once the cinematic triggered and Umbra escaped I could go back to my arsenal and re-equip Excalibur Umbra by choosing that loaout slot. 

I didn't try it but it seems like I would've been able to chase down Excalibur Umbra while already using Excalibur Umbra. 

[Daiwulf]

I was using Volt when I crafted/equipped Umbra, and after the scene I went back to the arsenal as operator, then it appeared the equipped Umbra in the menu but the Volt model in the background. (Didn't create an extra loadout for him, he was already there in the active one when I opened the arsenal)
Checked and I had the Excalibur, the sword already equipped and the umbral mods. 
When exiting, it changed to Umbra, then I came back and customized his appearance/mods.

And yes, I hunted Excalibur Umbra while using customized Excalibur Umbra and it was hilarious (those sentients didn't stand a chance against the umbral mods + exalted blade).

By the end of the quest, the customization I made to him was still applied, so the items didn't refresh in the inventory (I was hoping I would get another copy of the frame+weapon+mods at the end of the quest, but it didn't happen... sad☹️)