Yes, that's fine. I know it's tempting to hyphenate all verb-based compound adjectives, but I don't think it's necessary here. However, some people do hyphenate it as "fully-enclosed" (as the corpus I checked shows) and the sky didn't fall!
Where a hyphen is undoubtedly required, though, is for disambiguation purposes. For example, if I wanted to say that Ed is a reporter and that he has travelled a lot, I have two choices:
(1) Ed is a well-travelled reporter.
(2) Ed is a well travelled reporter.
In (1) the hyphen serves to indicate that Ed has travelled and that he has done so extensively; there's no doubt as to what is meant - it's just one adjective describing Ed. By contrast, the omission of the hyphen in (2) might give rise to the wrong interpretation since it could be understood to mean that Ed is both well and that he has travelled, thus two adjectives describing Ed. That's what we mean by employing a hyphen to avoid ambiguity.
But in your example, the omission of a hyphen in "fully enclosed" causes no such ambiguity. Though there may very well be "an enclosed shopping centre", there could hardly be a "fully shopping centre", could there?
Yes, I understand you completely now. It makes one wonder why this hyphen is still used at all now that you have explained what function it serves. As you said, I suppose it is just habit to join these terms together. They just seem disconnected without the hyphen.