No. The bible says Ishmael went east and was the progenitor of the Arab people. However, this was more than 2500 years before the birth of Mohammed and the founding of Islam. In the Christian Old Testament, of course a mirror of the Hebrew scriptures, when God's name is used it is written LORD in all capital letters. The Hebrew writers thought the name of God was so holy they would not write the vowels in it so we're not sure exactly what it is, but it's believed to be either Jahveh (Yahweh) or Jehovah.
There is no indication to my knowledge the Arab people ever worshipped Jehovah. Jehovah said he is God and there are no others. Mohammed was born into a society that worshipped several hundred gods. There were stones that represented each of these gods. Mohammed picked out the stone of one of these many gods, the moon god, and declared him to be the god of his religion Islam, thus the crescent moon as the symbol of Islam.