Yes. Our older lady has been free to roam the house since she was probably 18 months (same as yours). We started by crate training (right from the start, the day she came home to us). It has always been her bed and safe space, and never a punishment. When she was young, we crated her when we left the house, so that she would stay "honest" about her house training. And also to keep her from getting on furniture without human oversight present. By maybe 1year to 1.5 years old, we started letting her stay out of her crate if we were only going to be gone for an hour or less. She did bark at the window as we left in the beginning (when we first left her out of the crate). I think b/c the house was big, she was not confined in her "safe" space, and she could view us leaving. It created anxiety.
I was a SAHM at the time, and was rarely not home for more than an hour or so at a time, so it was not something she was accustomed to (being alone). We moved into a townhouse (while building our next home) for about 10 months right around that age, and the space was much smaller. She didn't seem nearly as anxious there. In general, I think it was because the space overall was smaller, and more confined (less open area). Her favorite spot was on the turn in the stairway, where she could see/guard both upstairs and down simultaneously, and the view was straight down into the front door.
Once we left there, we moved to where we are now. @2400 sq ft, and she still slept in her crate at night (with the door open). But we let her roam when we weren't home. She discovered the best place was to watch the front yard through the dining room window (low sash). It quickly became "her" spot. She only barks at activity outside, or unusual noises (if the neighbors the next street over have a party and the stereo bass booms loud enough to be heard at the window--even though *we* don't hear it inside.... she does).
She'll be 13 next month. About 8 years ago, I finally just put her crate in the attic. She had stopped sleeping in it at night (when we rearranged the master bedroom there wasn't room for it on my side of the bed anymore), and so we just put a regular dog bed on the floor and she sleeps there. We don't bother trying to contain her inside anwhere. (she actually can open all the interior doors anyway, so it's pointless unless you lock them, too.) But she doesn't get into anything. Mostly, I just put an old blanket on the sofa, b/c in her senior years, she has taken to giving herself permission to nap on the sofa when no humans are home. :P
(I work about 25 hours a week now, and she spends more time at home alone now than she ever has before. But she mostly sleeps these days. She's nearly 81 in people years.)
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ETA
I would keep doing what you are with the gate for now. It sounds like it helps with the anxiety. Over time, he will probably become more acclimated. 1.5 years in most breeds is still just a teenager. Adulthood often calms them down. So don't give up. I don't know what your routine is, but one thing we have done from the beginning is to use phrases. We used the same phrase/words to cue her to use the bathroom. The same phrase/words to have her sit. And so on... You are cueing her what is expected... both for her to expect to happen and also what you expect of her. So, if you don't, choose a "parting phrase" to use whenever you leave the house. That will cue her that a) you will be away from her for a while and b) that you will come back. In the beginning, maybe do it when you are only outside for 10 minutes, and then come back. If you can, wait until she is calm (not barking) and then come back while she is being well behaved.
We tell our girl, "Watch the house, we'll be back." Or if I'm leaving and my husband will be back before I am, I say "[husband's name] will be back." She knows us by name. :) So maybe come up with a phrase you ALL use every time so she can learn what to expect. It is helpful (just like with children) for them to know what is about to happen.