From observing my own enlightened Master and being around him, yes, it is correct that the enlightened ones are free from the push-pull of desire. Desire may exist, for example, one may desire to eat when hungry, but it can be more accurately described as a state of
choiceless awareness.
As the Buddha said, "events happen, deeds are done, but there is no individual doer thereof". The
Ashtavakra Gita is the purest expression of this type of spiritual teaching, one which I embrace myself.
In my opinion, the Abraham-Hicks type material is focused on material/emotional fulfillment, but as you correctly pointed out, desires only beget more desires; there's no end to it. It's a smarter option to realize the true nature of our Being, and then live life content and happy, whether we remain beggars, or become millionaires.