Reword your question as follows, and I would answer, “Yes.”
Gabe quoted the verses which indicate God does such things:
Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith will save the one who is sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven. Therefore, confess your sins to one another and pray for one another, that you may be healed. The prayer of a righteous person has great power as it is working. Elijah was a man with a nature like ours, and he prayed fervently that it might not rain, and for three years and six months it did not rain on the earth. Then he prayed again, and heaven gave rain, and the earth bore its fruit. (James 5:14-18)
Do you think God would have sent that drought in Elijah’s day anyway even if Elijah had not prayed? And would God have sent the rain later anyway? I think not.
However, prayer is not like a magic spell by which you can call up a genie and get 3 wishes granted. God does what He likes.
But when we make our requests known to Him, and sincerely ask Him to answer, He sometimes does. God wasn’t compelled to answer Elijah’s prayers. There are Biblical records of cases when He didn’t grant requests made in prayer.