No, God doesn't "need" wealthy people to get His work done, whether it's through churches or through other ministries. Most organizations (including ours) rely mainly on people who can only give a small amount of money -- but who are faithful in their prayers.
Does that mean God can't use wealthy people, or that their help isn't important in getting His work done? No, of course not. God has entrusted some people with significant resources, and their gifts can make a major difference to a project. To the best of our knowledge, Jesus never asked for money (although that doesn't mean it's wrong to do so). But a number of people of wealth supported His work, and without them His ministry might have been hampered (see Luke 8:3).
The Bible, however, repeatedly warns us against the dangers of wealth, and urges us to be content with whatever God gives us. Why is this? One reason is because money can easily take over the center of our lives -- a place that belongs only to God. In addition, greed can creep into our lives (even as Christians), overwhelming us and tempting us into paths we shouldn't follow. Jesus warned, "No one can serve two masters.... You cannot serve both God and Money" (Matthew 6:24).
My question to you is this: Are you serving God with the gifts and abilities He has given you -- not just with your money, but with your whole life? Put Christ first, and make it your goal to live for Him.