No, it is only a 2nd year tree and notoriously stingy with fruiting. I had a graft for a couple years that didn't fruit either. From what I can see, it has some flowers, but not many. I had heard that it is hard to get fruit in areas which aren't hot, so I put it right next to my driveway, with very close to full dawn to dusk sun. I also grafted another variety on (and have 2 others 5' away) to help with pollination. Add in a bit of branch bending...Even so, it may be a bit of a long-shot.
Speaking of flowers, in the last week mine have finally started to set for at least a few varieties (So and Honey Jar so far). They are in the tiny-acorn stage and there are lots of pollinators (ants, tiny bees and wasps).
That's not a bad thing. I'm actually pretty happy with the shape my So took naturally. It is about 8' tall by 8' wide.
Well, if you already have Sugar Cane, Honey Jar, and Li, then I would think that Contorted (zig-zag structure, also called So) and Shanxi Li (large fruit) might also be interesting. Both are offered by Bay Laurel, which I think uses the same supplier as the EL HJ. There are other varieties to add (Sihong, Autumn Beauty, and Redlands), but they aren't sold by any nurseries I know of, other than JFaE (the first 2 at least), and they have been out of stock for a year or more. But, given the good growth you see, you should have plenty of spots to graft to.