The website describing Ogden's Basic English is here.
Wiktionary has the 850 word list here.
I would argue that Basic English is a (rather) well defined invented language. Wikipedia lists it as a controlled natural language, which simply means that it is a natural language whose natural form and evolution have been suspended and its new form and evolution have been created by someone. In this case, Charles Ogden.
Classical Latin I have seen argued is a similar beast: a natural language that has some constructed or artificial tendencies, just not a single author.
The controlled language is, I would argue, the "fourth axial point of the Gnoli Triangle" --- the point where the art, science/engineering & practicality of invented languages become cotangent with the world of natural languages.
Basic English and its relatives might thus be seen as "conlang-natlang creoles". Where the creolisation process happens between two types of language rather than between two specific languages.
As for existing on its own, I think that is a rather different matter. If we were to replace the grammar with some kind of fundamental rule list and replace the English lexicon with unique, perhaps even levelled-Germanic words, we'd basically end up reinventing Esperanto. Or Folksprak. As such, yes, it could "exist on its own".
But Basic English is quite different among auxlangs, in that its essential function is that of a "bridge language". It is designed to bring people who have no English at all across the gap and to a place where they can immerse themselves in the broader Anglophone world. Basic English is thus, in this key regard, self limiting in scope and usefulness. It's great so long as the learner has extremely limited access to English speakers or English media.
As soon as that learner discovers the Internet or Anglophone aural culture (radio, television, movies) or English literature (broadly defined as anything written), they are going to discover the limitations imposed by Basic English. They'll have to leave it behind. In that sense, Basic English can't really have its own existence.
To build on your example: a Basic English speaker would simply have to step off the bridge and begin learning the "extended" lexicon of ordinary English!
