Yes, but Muhammed claimed that Ishmael settled in Mecca, not Paran as stated in Genesis 21:21
While he was living in the Desert of Paran, his mother got a wife for him from Egypt.
The Bible locates Paran near Israel (Canaan) and Egypt, south of Judah. John L. McKenzie in his Dictionary of the Bible notes:
Paran (Hb pa'ran, most frequently the name of a desert region). The place name Elparan (Gn 14:6) no doubt is associated with the desert; this place is thought to be identical with Elath by some scholars. The desert of Paran was the home of the Ishmaelites (Gn 21:21). It was, the itinerary according to P (cf. PENTATEUCH), reached by the Israelites after the desert of Sinai (Nm 10:12), and they camped in this desert for some time (Nm 10:12; 13:3, 26, mission and return of the scouts). In Dt 1:1 Paran is vaguely defined as a place in the desert. Hadad of Edom passed through the desert of Paran on his journey from Midian to Egypt (1 Kings 11:18). The mountains of Paran are the place from which the theophany appears (Dt 33:2; Hab. 3:3); like most other names mentioned in the theophanies, Paran reflects the region S of Judah. The desert of Paran is probably that region of the Negeb which lies S of Kadesh-barnea.
Compare this with other OT scripture:
"In the fourteenth year, Kedorlaomer and the kings allied with him went out and defeated the Rephaites in Ashteroth Karnaim, the Zuzites in Ham, the Emites in Shaveh Kiriathaim and the Horites in the hill country of Seir, as far as El Paran near the desert. Then they turned back and went to En Mishpat (that is, Kadesh), and they conquered the whole territory of the Amalekites, as well as the Amorites who were living in Hazazon Tamar." Genesis 14:5-7
"On the twentieth day of the second month of the second year, the cloud lifted from above the tabernacle of the Testimony. Then the Israelites set out from the Desert of Sinai and traveled from place to place until the cloud came to rest in the Desert of Paran. They set out, this first time, at the LORD's command through Moses." Numbers 10:11-13
"So Miriam was confined outside the camp for seven days, and the people did not move on till she was brought back. After that, the people left Hazeroth and encamped in the Desert of Paran." Numbers 12:15-16
"The LORD said to Moses, "Send some men to explore the land of Canaan, which I am giving to the Israelites. From each ancestral tribe send one of its leaders.' So at the LORD's command Moses sent them out from the Desert of Paran. All of them were leaders of the Israelites." Numbers 13:1-3
"At the end of forty days they returned from exploring the land. They came back to Moses and Aaron and the whole Israelite community at Kadesh in the Desert of Paran. There they reported to them and to the whole assembly and showed them the fruit of the land. They gave Moses this account: 'We went into the land to which you sent us, and it does flow with milk and honey! Here is its fruit.'" Numbers 13:25-27
"These are the words Moses spoke to all Israel in the desert east of the Jordan-that is, in the Arabah-opposite Suph, between Paran and Tophel, Laban, Hazeroth and Dizahab. (It takes eleven days to go from Horeb to Kadesh Barnea by the Mount Seir road.)" Deuteronomy 1:1-2
Surely, you're not suggesting that during the 40 year desert wandering of Moses & the Israelites that they travelled from Sinai all the way to Mecca and back?
"Now Samuel died; and all Israel assembled and mourned for him. They buried him at his home in Ramah. Then David got up and went down to the wilderness of Paran." 1 Samuel 25:1
Should we assume David travelled to Mecca, as well?
Though it may be true that some of the descendants of Ishmael settled in Arabia, that doesn't mean they were necessarily the father of Arabs. In fact, Muslim tradition affirms that Ishmael was not the father of Arabs:
Ishmael is the son of Ibrahim (Abraham) b. Tarih (Azar) b. Nahur b. Sarugh b. Rau'u b. Falikh b. 'Aybar b. Shalikh b. Arfakhshadh b. Sam (Shem) b. Nuh (Noah). (Ibn Ishaq, The Life of Muhammad, tr. Guillaume, p. 3)
'Ad b. 'Aus b. Iram b. Sam b. Nuh and Thamud and Jadis the two sons of 'Abir b. Iram b. Sam b. Nuh, and Tasm and 'Imlaq and Umayan the sons of Lawidh b. Sam b. Nuh are all Arabs. Nabit b. Isma'il begat Yashjub and the line runs: Ta'rub-Tayrah-Bahur-Muqawwan-Udad-'Adnan. (Ibn Ishaq, The Life of Muhammad, tr. Guillaume, p. 4)
This demonstrates that Arabs existed long before Ishmael was even born since according to this tradition, Ishmael's great-great-great-great-great uncles were already the Arabs!