Does SN44.9 imply an intermediate state between births? According to Kutuhalasala Sutta (SN44.9), translated by Thanissaro Bhikkhu:


  Vacchagotta: "And at the moment when a being sets this body aside and is not yet reborn in another body, what do you designate as its
  sustenance then?"
  
  Buddha: "Vaccha, when a being sets this body aside and is not yet reborn in another body, I designate it as craving-sustained, for
  craving is its sustenance at that time."


Alternative translation by Bhikkhu Bodhi here:


  Vacchagotta: “And, Master Gotama, when a being has laid down this body but has not yet been reborn in another body, what does Master
  Gotama declare to be its fuel on that occasion?”
  
  Buddha: “When, Vaccha, a being has laid down this body but has not yet been reborn in another body, I declare that it is fuelled by
  craving. For on that occasion craving is its fuel.”


In the Theravada tradition, the orthodox doctrine based on the Abhidhamma states that there is no intermediate state between births, that rebirth-linking consciousness instantaneously results in a new birth without any gaps.

However, the above sutta implies that it is possible to have an intermediate state that is sustained by craving.

So, my question is: does SN44.9 imply an intermediate state between births, or is there an alternative interpretation for it?
Piya Tan has an essay on the topic here: Is Rebirth Immediate? (SD 2.17)

And a commentary and translation of the sutta here, Kutūhala,sālā Sutta, which includes "To Vaccha’s second and final question, the Buddha makes his famous statement on the intermediate state."

My paraphrase of the essay (if I've read it correctly) is that:


The Abhidhamma and commentaries denies an intermediate state, on not very strong grounds (e.g. that the Buddha didn't teach explicitly that there is such a thing)
Many people (Theravada and other schools) believe in such a state anyway
There are suttas (which it quotes) which may be describing an intermediate state
Other sources include the Chinese Agamas, and the Sanskrit, the Milinda Panha


That essay totals about 15 pages -- you can read the details.

It quotes Ven. Sujato's commentary on The Kutūhala,sāla Sutta:


  From this we can conclude that the Buddha, following ideas current in his time—for Vacchagotta
  was a non-Buddhist wanderer (paribbājaka)—accepted that there was some kind of interval
  between one life and the next. During this time, when one has “laid down” this body, but is not
  yet reborn in another, one is sustained by craving, like a flame tossed by the wind is sustained by
  air. The simile suggests, perhaps, that the interval is a short one; but the purpose of the simile is to
  illustrate the dependent nature of the period, not the length of time it takes. While a fire is burning
  normally, it is sustained by a complex of factors, such as fuel, oxygen, and heat. But when a
  tongue of flame is momentarily tossed away from the source fire, it can last only a short while,
  and in that time it is tenuously sustained by the continued supply of oxygen. Similarly in our
  lives, we are sustained by food, sense stimulus, and so on, but in the in-between, it is only the
  slender thread of craving that propels us forward. The difference is, of course, that the flame will
  easily go out, while the fuel of craving propels the unawakened inexorably into future rebirth.