Did Arabs live in Palestine before the 7th century Arab invasion ?

Yes.
The Qedarite and later on the Nabataean kingdoms ruled over Jordan, Palestine and Sinai a whole millennium before Muslims ever set foot in the area. Another example would be the Ghassanid kingdom, which was a Christian Arab kingdom that extended over vast areas of the region. As a matter of fact, many prominent Christian families in Palestine today, such as Maalouf, Haddad and Khoury, can trace their lineage back to the Ghassanid kingdom.
Arab populations had existed in Palestine before the conquest, and some of these local Arab tribes and Bedouin fought as allies of Byzantium in resisting the invasion, which the archaeological evidence indicates was a ‘peaceful conquest’, and the newcomers were allowed to settle in the old urban areas.
The term “Arab”, as well as the presence of Arabians in the Syrian Desert and the Fertile Crescent, is first seen in the Assyrian sources from the 9th century BCE.
Southern Palestine had a large Edomite and Arab population by the 4th century BCE.
Inscriptional evidence over a millennium from the peripheral areas of Palestine, such as the Golan and the Negev, show a prevalence of Arab names over Aramaic names from the Achaemenid period,550 -330 BCE onwards.
The Qedarite Kingdom, or Qedar(Arabic: مملكة قيدار‎, romanized: Mamlakat Qaydar, also known as Qedarites), was a largely nomadic, ancient Arab tribal confederation. Described as “the most organized of the Northern Arabian tribes”, at the peak of its power in the 6th century BCE it had a kingdom and controlled a vast region in Arabia.
Qedarite kingdom in the 5th century BCE
Biblical tradition holds that the Qedarites are named for Qedar, the second son of Ishmael, mentioned in the Bible’s books of Genesis (25:13) and 1 Chronicles (1:29), where there are also frequent references to Qedar as a tribe.
The earliest extrabiblical inscriptions discovered by archaeologists that mention the Qedarites are from the Neo-Assyrian Empire. Spanning the 8th and 7th centuries BCE, they list the names of Qedarite kings who revolted and were defeated in battle, as well as those who paid Assyrian monarchs tribute, including Zabibe, queen of the Arabs who reigned for five years between 738 and 733 BC.
There are also Aramaic and Old South Arabian inscriptions recalling the Qedarites, who further appear briefly in the writings of Classical Greek, such as Herodotus, and Roman historians, such as Pliny the Elder, and Diodorus.
It is unclear when the Qedarites ceased to exist as a separately defined confederation or people. Allies with the Nabataeans, it is likely that they were absorbed into the Nabataean state around the 2nd century CE. In Islam, Isma’il is considered to be the ancestral forefather of the Arab people, and in traditional Islamic historiography, Muslim historians have assigned great importance in their accounts to his first two sons (Nebaioth and Qedar), with the genealogy of the Islamic prophet Muhammad, alternately assigned to one or the other son, depending on the scholar.
The Arab city of Abdah in the Naqab desert, predating Islam and 7th century conquests by 800-900 years.
Idumean (Identified as one with the Nabatean Arabs by Greek Historian Strabo) Arab ruins outside Beit Jibrin in Palestine (6th century BC) predating the arrival of Islam by about 1200 years.