No. Do not reward criminal behavior. Deport all illegals, no exceptions. Before they leave, take their fingerprints and DNA, and permanently bar them from any path to legal entry or citizenship. Fine them everything they have to cover the costs of enforcement and deportation. Fine their employers for failing to check citizenship and status. No exceptions.
Then we can reform the legal immigration system to bring in the number of legal immigrants that will benefit Americans, specifying qualifications and origin.
I have heard this somewhere before maybe someone running for President said it?