Frequently, although it depends a bit on what you mean by eastern and western Romans.

Prior to the establishment of separate eastern and western portions of the Empire under Diocletian, there were at least two times that generals led eastern armies into Rome to seize the throne:

Vespasian in 69 (defeated the forces of Vitellius) Septimius Severus in 193 (filled the power vacuum left but he assassination Didius Julianus)

But I don't think that's what you were asking.

The first formal division of the Roman Empire into an Eastern and Western parts under Diocletian in 286. Feeling that the Empire was too unwieldy for one man to rune effectively, Diocletian established the Tetrarchy. The Empire was divided into Eastern and Western halves, each with an Augustus to rule. Each Augustus would have a junior partner known as a Caesar. The idea was that the Augusti would rule for a limited time and abdicate in favor of their Caesars, who would then appoint new Caesars to take their place, and so on. The system worked about as well as you might expect one involving 4 ambitious men sharing nearly absolute power would work. Diocletian did in fact retire in 305, and essentially browbeat his co-Augustus Maximian to abdicate along with him.

The next 19 years consisted of a series of combinations of the Augusti and Caesars fighting each other. During that time, eight men claimed the title of Augustus at some point, including the reluctant abdicator Maximian who twice tried to come out of retirement back to power. Five of these men either were killed in battle or were executed/forced to commit suicide after losing a battle with one of the others. When the dust settled, Constantine the Great was sole ruler, and things were peaceful, with a reunited East and West, until Constantine's death in 337.

Things fell apart quickly thereafter, as Constantine's three surviving sons proved unable to share the joint rule they had been placed in. The brothers fought, and East and West came into conflict again. Constantius II came out of top in 350, and he and a couple of his successors maintained sole rule until 364 when rule was formally split again. From this point on, except for a brief three year period under Theodosius I from 392-395, there were separate rulers in East and West until the western parts fell, with the formal date of the fall typically cited as 476. During this period there were occasions in which the eastern emperor went west to do battle with a western emperor (Theodosius over Magnus Maximus in 388, Constantius III over Constantine III in 421).

A coda to the Eastern vs Western Roman Empire occurred in 535 when the Emperor Justinian I ordered the reconquest of Italia under his general Belisarius. But by this time, Belisarius was fighting Ostrogoths, and the only Roman Empire was in the East.