Strictly speaking, "Allah" is simply a contraction of the Classical Arabic word "al-Ilah", meaning "the god" (related to "Elohim" in Hebrew). In pre-Islamic times, Allah was probably one of a pantheon gods worshiped at Mecca, but it was also the word Arabic-speaking Christians used to mean God, yes. Evidence of this has been found in inscriptions in a church in Umm al-Jimal, Jordan.

Sources:

• Christian Julien Robin, "Arabia and Ethiopia," in The Oxford Handbook of Late Antiquity, ed. Scott Fitzgerald Johnson. Oxford University Press USA, 2012: p. 304.
• James Bellamy, "Two Pre-Islamic Arabic Inscriptions Revised: Jabal Ramm and Umm al-Jimal", Journal of the American Oriental Society 108, no. 3 (1988).