I think you're over-thinking this, and with all respect to everyone else trying to help, I think the answers focusing on depth of field equivalence calculations are making things worse. No one is wrong — I just think it's leading in the wrong direction. Let me suggest a different approach.
The crucial thing first: you will absolutely be able to make photographs with this lens on your camera where your subject's nose is in focus but their ears are not. Or more usefully, yes, with this lens and your camera, you can get meaningful separation from your subject and a background, perhaps blurring out a busy background so it does not distract from your subject.
By all accounts, this is a lovely portrait lens. If that's what you are looking for, and the economics work out for you, then it is absolutely "worth it".
But what about this depth of field that could be even more shallow on full frame? Well, it would be even more shallow on medium format. Worrying about that doesn't provide you with any value. What's your alternate? To stick with slow lenses? That would be silly, like, "My car isn't a Formula One racer, so I only drive at 15mph."
Or perhaps you meant, do I need a faster lens? Well, again, not to get great bokeh and background separation. (In fact, you have plenty of room to stop down from f/1.4 and still get that.) If you do, your one alternative is the Mitakon Zhongyi 85mm f/1.2 — no one else makes a faster 85mm lens for Nikon. And that lens has some interesting, positive reviews, but is manual focus and makes a great deal more optical compromise than the Sigma Art lens. So maybe you want that, but — it's not necessary.
In general, there's a lot of mysticism around full-frame on the Internet. Full-frame isn't magic, and isn't the pinnacle of photographic options. It's just a larger sensor size than APS-C — and smaller than medium format, and smaller still than a whole host of historical film formats. It's true that this lens happens to be usable on modern cameras in both APS-C and full-frame formats (DX and FX, in Nikon terms), but that's really just a quirk and shouldn't hold you back.
On this site, a photograph is worth more than a thousand words, so let me present some examples to demonstrate the point. I did a quick search on Flickr and came back with a few.
This one was shot on an APS-C Canon camera (sensor slightly smaller than Nikon APS-C), on a Sigma 85mm f/1.4 lens:
... and that's actually stopped down a tiny bit to f/1.6!
Or here's one on a Pentax K100D (a camera from over a decade ago) — it's a different 85mm f/1.4 lens, but the basics of depth of field are the same:
And here's one on a Nikon D80, again with some other 85mm lens, but, also again, the basic idea is illustrated:
You can find more examples pretty easily. In short, this lens can definitely do what you describe wanting. Of course, whether spending for what you want makes sense is a personal decision no one else can make for you, but my sense is that you won't regret it.