Can a document contain its own hash? Do any methods exist whereby a "hash" can be embedded in the "document" it hashes?

What I mean is this. Say I have a given plaintext T. I wonder if there is a method to craft (i.e. not discover as a fluke) a "document" D being some combination  (e.g. a concatenation) of T and a hashvalue h, where h is H(D), H being some hash function.

Perhaps a simpler way of phrasing this is: Is there any way to make a document contain its own hash, under the constraint that the document must, apart from its own hash, contain a given plaintext?

Is this possible in theory? In practice? 

This question is somewhat different from this one, in that I am assuming a given plaintext T, whereas that question asks if any T can be crafted (or found).
It actually depends on what you consider a hash function.

If we take a CRC (Cyclic Redundancy Check) as our hash function, then it is quite feasible; a CRC has a property that every output bit is a linear (affine if the initial state is nonzero, but the difference is unimportant) function of the input bits; hence we can generate a set of linear equations over the various bits of X in the expression $CRC( Message || X || MoreMessage ) = X$, and attempt to solve that (and find the solutions, if any).

I would further note that CRC does meet the criteria you gave; it can potentially have a large range (just make the CRC state large enough), and at first glance, if you just look at inputs and outputs, it does appear random.

Of course, a CRC is not a secure hash function; however you didn't specify a secure hash function.