My impression is that, although most people prefer not to use a hyphen here, it is not necessarily completely unacceptable to hyphenate "well-organized" in this context.
A hyphen could be supported by analogy with phrases like "well-known", which dictionaries such as Collins indicate may be used with a hyphen even in predicative position:
If someone is well-known for a particular activity, a lot of people know about them because of their involvement with that activity.
- He is well-known to the local police.
- Hubbard was well-known for his work in the field of drug rehabilitation.
- It is well-known that bamboo shoots are a panda's staple diet.
Something or someone that is well-known is famous or familiar.
That said, Collins in fact indicates that the spelling "well organized" is or should be used in this context:
well organized when postpositive
So the issue of how to hyphenate adjective phrases of this type in this context is a little unclear. (Hyphenation is one of the less consistent areas of English orthography.)
I wrote an answer to a related question, Hyphen: “well defined” vs. “well-defined”, that I think is relevant. Here is a portion of it (slightly modified):
As described in Sven Yargs's answer to the following question (Should there be a hyphen in expressions such as “currently-available X”?), hyphens are generally only avoided after the adverb very, or after any adverb ending in -ly. There is no generally observed rule that I am aware of forbidding the use of a hyphen after other kinds of adverbs, such as well, quick, hard.
There are many phrases starting with "well" that are commonly hyphenated, mostly ending in participles or departicipial adjectives, like well-read and well-known. (Examples starting with other adverbs: quick-thinking and hard-working).
The hyphenation of adjective phrases in predicative position seems to be a bit more variable than that of adjective phrases in attributive position, but using a hyphen in this kind of context is considered correct by at least some stylebooks:
These sentences are both correct:
Supporting the distinction above are Garner's Modern American Usage, The Chicago Manual of Style, and The Gregg Reference Manual.
But well-known is also acceptable in both sentences according to The Associated Press Stylebook (AP). The rule in AP is that "when a modifier that would be hyphenated before a noun occurs instead after a form of the verb to be, the hyphen usually must be retained to avoid confusion." AP gives this example: "The man is well-known."
So, I hope the answer is now well known to you: Both well-known and well known are correct. You choose.
–"A Well-Known Problem: Well Known", by Lynn Gaertner-Johnston, Business Writing Blog
The Corpus of Contemporary American English has 21 results (excluding spoken examples) for "is well organized" (8 from magazine articles, 5 from newspaper articles, and 8 from academic texts) vs. only 6 for "is well-organized" (4 from newspaper articles and 2 from academic texts).
I excluded spoken language examples because I assume their classification just represents the choice of the transcriber, but there were 3 for "is well organized" and 2 for "is well-organized".