Is it possible to add site links which are not stored in Wikidata?
Topic on Talk:Beta Features/Other projects sidebar
That is currently not possible. Would be good to make that possible though as that is something Wikivoyage for example could really use.
At Wikivoyage we use an extension to present links to external websites like Wikipedia, Commons, DMOZ in the sidebar. In the source code you will find codings like [[wikipedia:anything]], [[commons:Category:anything]], or [[dmoz:anything]]. In the sidebar a section named "Related sites" appears giving the links to Wikipedia, Wikimedia Commons, and DMOZ, respectively.
Of course, this is similar to the section "Related projects" proposed as a beta feature. But not all properties are stored in Wikidata, and therefore we need a similar tool like {{#addproject:DMOZ|http://www.dmoz.org/World/Deutsch/Regional/Afrika/%C3%84gypten/}} or {{#addproject:Wikimedia Commons Category|https://commons.wikimedia.org/wiki/Category:Egypt}}. The first parameter in this example shows the link text, the second one the link itself. You can see that we need it also to present related Commons categories at least in the case of a missing corresponding Commons article. In this respect, there is no answer in the topic below "Commons main and category namespaces".
If we want to substitute the RelatedSites extension we need a tool which has in any case the same functionality.
Are there cases where the data couldn't go into Wikidata that is currently used in the sidebar?
It's possible that there are cases where there isn't a 1:1 correspondence, much like inter-language links where and were both linking to at one point. (That specific instance was resolved when fr: split its coverage of Ottawa-Hull into two articles.) Wikidata will not allow two items to link to the same target.
At the German Wikivoyage we use now "Related sites" extension mainly in the User namespace because "other projects" is not supported by Wikidata. It is no problem to link to other languages but to link to other projects.