No.
They will ask you:
Was this degree, diploma or certificate:
-from a public post-secondary school, such as a college, trade/technical school, university or CEGEP (in Quebec)
-from a private post-secondary school that operates under the same rules as public schools
-a diplôme d'études professionnelles (DEP) or an attestation de spécialisation professionnelle (ASP) earned through a qualifying -study program of at least 900 hours from a private school in Quebec, or
a Bachelor's, Master's or Doctorate degree from a Canadian private school that can legally award degrees under provincial law. (The student must have been enrolled in a study program that led to a degree as set out by the province.)
Private colleges in general DO NOT follow the same rules as public schools so you are not eligible for the Canadian education points. The DLI does not mean anything on this regard.
You can still get the normal points for the diploma though.