I just realized how old this question is after wasting my time answering a ghost. Sigh... Oh well.
In some of the stories I've read, one's wife is referred to as one's "costilla" and one's children are referred to as "los pecados". In others, one's sister is named
(this is possibly obscene, I'm not sure)
So it wouldn't be surprising if there had been a humorous connection. The reality is the English came from French "embarras du choix" or hindrance from having so many choices because you're so rich that it's embarrassing. Which came from latin "in"+"barra" meaning "into the bar" for obstructed.
The same question was answered here; however, the author who cites the Royal Spanish Academy did not seem to think the connection between the Latin etymological root from the link above was the origin:
[Embarazar] came from the Portuguese embaraçar, and the Royal Spanish
Academy theorizes that word originated from Celtic because its root
palabra existed before the Romans conquered the Iberian Peninsula.
However this same author states the following, despite the obvious connection between being blocked up/obstructed and pregnant:
Why a word that signifies a blockage came to represent pregnancy is
unknown to etymologists
Therefore it might be necessary to find the un-cited reference directly if you're concerned about whether the root is celtic or latin.