I believe He could, though He wouldn't be happy about the false aspects of the religion. He looks on the heart, and answers prayer according His kind intentions, which preeminently have to do with leading men to Christ.

Primarily, only God can answer that question, if He wills to respond to such a prayer, obviously knowing all things, including that the prayer is made, then in His wisdom, He will respond to such a prayer. Only God can answer that for any individual instance, though I personally am of the opinion that there are some faithful Hindus who, only through the grace of Christ, are charitable individuals, and consequently I am sure that God does answer their prayers, at least from time to time.

The Lord is far from the wicked, but he hears the prayers of the righteous. (Proverbs 15:29)

Your iniquities have made a separation between you and God, and your sins have hidden his face from you so that he does not hear. (Isaiah 59:2)

We know that God does not listen to sinners, but if anyone is a worshiper of God and does his will, God hears them. (John 9:31)

If anyone turns his ear away from hearing the law, even his prayers are an abomination. (Proverbs 28:9)

Do orthodox Christians believe God would hear and answer a prayer if it were made to for example the Hindu God Shiva ?