Not quite. Allah may be Arab word for God, but I think it was co-opted into the Arabic; Allah predates Islam, Mohammad and Koran.
Allah was originally a Hindu Goddess. There is an Upanishad called Allopanishad (Upanishads are part of Hindu Scripture). Later the Goddess traveled to the Middle East. At the time of Mohammed, people in the Middle East used to worship many Gods, including Allah.
Mohammed decreed that all Gods except Allah are false Gods, and people must worship only Allah. Allah did not originate with Islam; it was an already existent God which was co-opted into Islam.
Allah in Arabic originally means Al-ilah: the god.
This word Allah is the synonym of God in English, Yahweh in Hebrew, Khodah in Persian and Kurdish, etc.
Of course the Quran was revealed in the language of the Arab; and the word Allah was used before the Quran to indicate the Creator Who is known to all people everywhere by different names according to their languages.
Allah or God is there before the Indian and before the Arab and before all people and all angels even.
These are names only and the named One is the same One.
In other words:
God has many names: Arabic, Hindu, Hebrew, English ...etc; but He is the same One: the Creator; while all other idols are false and invented.
This in the Quran 59: 22-24 about God or Allah:
هُوَ اللَّهُ الَّذِي لَا إِلَهَ إِلَّا هُوَ عَالِمُ الْغَيْبِ وَالشَّهَادَةِ هُوَ الرَّحْمَنُ الرَّحِيمُ . هُوَ اللَّهُ الَّذِي لَا إِلَهَ إِلَّا هُوَ الْمَلِكُ الْقُدُّوسُ السَّلَامُ الْمُؤْمِنُ الْمُهَيْمِنُ الْعَزِيزُ الْجَبَّارُ الْمُتَكَبِّرُ سُبْحَانَ اللَّهِ عَمَّا يُشْرِكُونَ . هُوَ اللَّهُ الْخَالِقُ الْبَارِئُ الْمُصَوِّرُ لَهُ الْأَسْمَاء الْحُسْنَى يُسَبِّحُ لَهُ مَا فِي السَّمَاوَاتِ وَالْأَرْضِ وَهُوَ الْعَزِيزُ الْحَكِيمُ
The explanation:
(He is God; there is no god [to be worshipped in the universe] but He.
He is the All-Knowing of all that is absent [: invisible and unknown to you], and all that is present [: visible and known to you];
He is the Most Gracious, the Most Merciful.
He is God; there is no god but He:
the Sovereign Lord,
the Sanctified [by His angels],
the All-Peaceable,
the Believer [in Himself],
the Dominant [over His creatures],
the Almighty,
the Compeller [of unbelievers to the Fire],
the Most Sublime [above His servants.]
Celebrated be God above all that they associate [with Him.]
He is God;
the Creator [of all the creation],
the Savior [of His loyal servants],
the Fashioner [of bodies inside wombs.]
His are the Names Most Beautiful.
All that is in the heavens and the earth glorify Him,
and He is the All-Mighty,
the Most Wise.)