I don't feel it's a matter of being "user friendly". It's a matter of presentation.
An incompletely design carries with it a stigma or connotation that you're okay showing off incompletel, unfinished work/products. If the site is customer-oriented (selling a product/service) this indicates that there's no attention to detail perhaps or maybe no follow-through by customer service. If the site is information based, incomplete or missing pages would carry a message of haphazard information or perhaps incomplete information in the areas which are presented.
It is best to complete any design before showing it off to the public. This is true for any project. You never show early stages or partial pieces until everything is complete. Then, and only then, you may want to show "how this was created" content in the context of how the (design) problems were solved.
Due to this you should never show any "under construction" page for any reason. Finish the design, then implement it. There's no reason to have a partial site presented.
If the goal is to get users interested in a "feature" add-on of an existing site while the feature is still being constructed, then a "teaser" page may be implemented. But this would never really be an "Under Construction" page. It should be a "sign up now" or "get notified" page -- so technically a page still.
The only exception may be an entire site as a "coming soon" page rather than some generic hosting landing page to be a placeholder between the domain/hosting being purchased and the site being pushed live. This may still be a bad idea if it can be avoided. Primarily because if a user hits an "under construction/coming soon" site they may never return to it or see it as a new start up and not be interested in someone's new venture. However, if a domain has been purchased and there is some remote possibility a user may inadvertently find that domain, any page is better than the registrar/hosts generic "someone bought this" page.
A generic "under construction" or "coming soon" page generally reflects poorly on the web site in all instances.