No, it’s not impossible to connect an external disk to home assistant and mount it into your immich addon. But it really defeats the ease of use of the immich addon itself, because if you don’t know what you’re doing you could really brick or erase your home assistant instance. It’s not as straight forward as it should be, so in my humble opinion is really just better to buy an old used nas, pop in a pair of spare drives (maybe in raid1) and mount it through the hassio ui.
But as it seems to be a very requested feature, I’ll think about it. Thanks for asking 
EDIT
So it just occurred to me, that nowadays almost every isp provide a router with at least one usb port that can be used to plug an external hard disk and use it also as a nas. 
I though you might wanna give it a try