Well, it's a bit of a tricky question. According to the available sources, which were all written centuries after the fact and look back at the period from a perspective in which Islam survived, thrived, and expanded, by Muhammad's death the Arabs had all be united under the banner of Islam. This was not entirely a form of conquest. The political order around the Peninsula had been breaking down before the advent of Islam and, as the Muslims became a dominant force, people sought them out for protection, support in local conflicts, etc. Again, according to our sources, immediately after Muhammad's death many Arabs apostatized and the first caliph (Abu Bakr) was forced to fight a war (the Ridda War) to reunite the Peninsula.

Modern scholars have looked back at this and have questioned the nature of the relationship between the tribes of the Arabian Peninsula and Muhammad (were they entering into a tribal confederation or accepting a belief system?) and even the nature of Islam during Muhammad's lifetime (was it clearly an organized system of beliefs or was Muhammad's position more that of a tribal shaykh).

For two books that tackle these tricky questions, check out...

Fred Donner, Muhammad and the Believers

Robert Hoyland, Fighting in God's Path