No, and therein lies the rub. ("reasoning by analogy" is a logical error.) Because the difference is key, and is outlined first by Deuteronomy 24:1 through 3 (and the process is repeated TWICE), and is clearly referenced by Yahushua.
What should be emphasized in this regard (and indeed, in general, on the topic) is that Matthew 5:31-32 (and the context!) does a better job of addressing the exact same issue. And it is easy to spot the HORRIBLE mis-translations there:
both by simply comparing different English renderings, and noting that the Hebrew word "shalach," which DOES mean to "put away," is rendered into the Greek 'apuolo,' MULTIPLE times. But, in at least some English versions (notably the KJV) also by noting that the very same word is translated into DIFFERENT English words (i.e., 'divorce') in error - even in the same verse!
A woman who has been 'put away' but does NOT have a 'sefer keretutah,' or 'certificate of divorce' (written witness) is STILL MARRIED. The implications of the rest of the verse then become obvious.