Short answer is no.

The reasons behind the splitting of the empire made complete sense at the time. Basically the progression of the idea was this. The empire was too large for one man to rule effectively so it became clear that delegation was required. However at the same time you sometimes needed an emperor to make certain decisions for example many of the strategic questions. So how could you rule an empire in this way. The answer was multiple Emperors with one nominally the higher ranked but otherwise they were in charge of their own territory to do with as they saw fit.

Now as to what effect did this have on the empire?

Far from destroying it the splitting saved it. Diocletian was the one that introduced the system and immediately prior to its introduction the Empire was in its most dangerous period in centuries. The crisis of the third century had seen a 50 year period where the longest reign of an Emperor was 8 years and over 14 emperors reigned. This period demonstrated that if two threats occurred at the same time then the empire could not function with one man.

Overall if these reforms had not taken place then the Empire likely would have fallen in the early 300s and it would have been the entire Empire not just the western half.

Sources

Aurelian and the Third Century Fall of the Roman Empire a new history Roman Empire Fall of the west survival of the east