No, it doesn't work that way at all. The amount of the credit declines with each $1,000 of your income, so at even a close amount to the income limits, your credit would be small.
This also is not a refundable credit, meaning it does not directly increase your refund. Rather, it is a subtraction from your taxable income, so what you save is the amount of tax you would have owed on that amount of income.
