The short answer is no, they are not people. The long answer is that the courts have long held that corporations, since they are made up of people, do have some of the rights and responsibilities as individuals because people don't lose their rights just because they act collectively. However, that means that each right needs to be reinterpreted in that light. Corporations do get the protections of free speech, for example, but courts have found that Fifth Amendment protections only apply to individuals (hence a corporation and its directors/shareholders/employees can be subpoenaed to provide documents and testimony incriminating the corporation).

This has nothing to do with the legislature or lobbying. It is a legal principle largely established by strict constitutionalists in the judiciary (aka conservative activist judges). Short of a sweeping Constitutional amendment, corporate personhood is entirely up to them.