No. if he signs over his rights, he gives up ALL rights, including any financial obligations, so you will not be able to collect child support if he does that. And, on the other side, if he decides in the future to want to see the child, you have no obligation to let him since he signed his rights away.
good luck. After me and my daughter's father split, we stayed with my parents, I worked full-time and went to school at night to finish my degree. It's tough, but you can do it! Never give up.