If he goes through Armenia, Artavasdes has a trick up his sleeve to sabatoge him. His whole strategy was to play the Romans and Parthians off each other-hell during that very war he joined the Parthians. He was responsible for the failure of Antony's campaign by slipping away back to Armenia and letting the baggage train get slaughtered.
Plus, Crassus took the desert route because of the offer he had received a similar offer from an Arab king in the area.
But anyway, let's say Crassus takes the same route and everything happens the same. Except instead of a fight breaking out at his parley with the Parthians and the resulting slaughter of his men, he is able to retreat back to Roman territory in good order. Congratulations, the triumvirate is saved. Pompey won't begin to turn on Caesar. Crassus was the glue that kept the triumvirate together.
edit: and the collapsing of the triumvirate at Crassus' late death won't necessarily mean a face off between Pompey and Caesar. Remember, the triumvirate was just an informal understanding between the three men, compared to the second triumvirate which was a legally binding agreement ratified by the Senate. So you will most likely just see the triumvirate slip quietly into the dustbins of history.
Not to mention, Caesar won't be in the same lose-lose situation he was in that lead him to roll the dice. Even if Pompey does the unlikely thing of backing him into a corner, Crassus will bail him out and find a way to let him run for consul again, or at the very least escape prosecution. Though Cato would really be a thorn in his side.