By crusades, I assume you mean the Crusades of the Middle Ages in which Western European powers attempted to wrest Jerusalem from the Muslims. Such being the case, they were not important to the Roman Empire because it had ceased to exist. The Roman Empire ended with the abdication of Romulus II Augustulus in 476 C.E. The first Crusade was preached by Pope Urban II at the Council of Clermont in March, 1095. Although Charlemagne had been crowned "Emperor of the Romans" in 800 C.E., even this had no connection to the Crusades. So, the answer to your question is, there was no importance, because one had ceased to exist before the other became extant.
Please note that there were not any Crusades during the time of the Roman Empire. The Crusades did not start until the late 11th century and the Roman Empire is usually said to have fallen in the late 5th century. In addition, the Crusades were fought against Muslims and the Muslim faith did not come to be until the 620s. Therefore, there could not have been any Crusades in the Roman Empire.
You have tagged this with "empire split." I wonder if you are referring to the fact that the 4th Crusade ended up taking not Egypt, like it was supposed to, but the city of Constatinople. Constantinople was the capital of the Eastern Roman Empire, which became the Byzantine Empire. By taking Constantinople, the 4th Crusade helped in a small way to further drive the Orthodox Church (in what used to be the Eastern Roman Empire) from the Roman Catholic Church (in what used to be the Western Roman Empire).
However, it is important to note that there were no Crusades during the time of the Roman Empire.