The short answer to this question is 'No'. Poetry is most often thought of as a structured literary form. The patterns of couplets, tercts and quatrains and device of enjambment that are referred to in this question are structural poetic devices.
However, Desiderata is a prose poem. The form of this type of poem when first seen on a page, may at first glance lead to an impression that the text is prose, as it does not have the rhymes and metrical rythms usually associated with poetry. The defining feature however, of a prose poem is that the text includes one or more poetic techniques and so,essentially, sounds like poetry.
Couplets,tercets and quatrains are unlikely occurences in prose poems, which are usually written in sentences and paragraphs - as is Desiderata.. Enjambment is a technique in which the idea in a line is carried through to the following line, or lines, without punctuation at the end of lines.This technique might sometimes be used in prose poems but you will notice that each line in Desiderata ends with a punctuation mark - each line makes complete sense and is a self-contained thought.
The main technique employed in Desiderata is repeated parataxis, which is described in my article.