Low voter registration and/or turnout does effect democracy, although it is difficult to measure this in any precise way. As a general rule, the fewer people who vote, the less likely they are to buy into what the elected leadership is doing. They are more likely to feel disenfranchised, in spite of the fact that they have disenfranchised themselves. They feel their interests are not being represented, which is, in fact, probably true. When people vote, they have a sense of "ownership" in the system, which makes them more involved and watchful, while those who do not vote are not such good guardians. This can cause abuses of power and possibly corruption on the part of elected leaders. Another negative consequence is that low voter turnout harms the mandate of the elected leader. When there is good voter turnout, a leader feels more empowered to lead, believing he or she is elected by the many, rather than by the few. This is better for a democracy than when we have a leader who has been elected by a small percentage of the people, since the leader will not really have a firm grasp of whom is being represented.
These are reasons that voter registration acts matter so very much. In the United States, we do not participate as well as we should or could in elections right now. And every time a state passes a law that makes it more difficult for people to vote, the lower the turnout is, and the worse this is for a democracy. We want greater participation in this system, not less, so that more people believe they have a stake in the system, so that people do not feel disenfranchised and act apathetically, and so that more of us are watching our leaders and empowering them to act on our behalf.