Yes, of course she should -- because without God's help, she would not have had the same outcome. One of the best-loved Psalms declares, "Even though I walk through the darkest valley... you are with me" (Psalm 23:4).
Why do I say God was helping her -- even if she didn't realize it? First, God gave the doctors their skills, and He also gave them the wisdom they needed to deal with her illness. In addition, God worked in response to the prayers of others. God also made our bodies, and He designed them so they could heal in response to the right medicines. The Psalmist's words should echo in each of our hearts: "I praise you because I am fearfully and wonderfully made" (Psalm 139:14).
Gratitude, I'm afraid, is the missing ingredient in too many lives -- gratitude to God for His goodness; gratitude for His care for us; gratitude for every gift He gives us. Thanksgiving shouldn't be just a once-a-year celebration! The Bible says, "Give thanks in all circumstances; for this is God's will for you in Christ Jesus" (1 Thessalonians 5:18).
Pray for your cousin, that she may realize just how good God has been to her. Most of all, pray that she will realize her need to put her life into His hands by committing herself to Jesus Christ. Some day -- like all of us -- she will die and enter eternity. May she do so with Christ in her heart.