Yes, you can test this without the app being in the store, although I think the validation tool will report this error since it doesn't know anything about this app.
At a glance, things do seem in order and I don't see anything out of sorts. What OS are you testing this with?
Also, where are you testing opening this URL? I'd recommend using Mail or Notes, since the handling of universal links in Safari can be a little confusing (the rules of when to open Universal Links sometimes trip people up. What I like to do is use Mail, tap-hold on a link to get the sheet of action buttons and then see if "Open in [app]" is in there. If it is then your Universal Links configuration is valid. If it's not, then the device is not recognizing your setup.
Thanks for your reply! I actually got it working. The validator still shows the error, which is odd since the app is on the App Store. But regardless, things seem to be working. I've posted another question related to Handoffs and Universal Links, and I would love to be able to get your response to that one if you can answer it. Thanks again!