To answer your first question, yes, if you're using a groove detail meeting those of 3.12 or 3.13.
However, this is not true of corner and T joints. See 4.10.1.1.
If you qualify your CJP single bevel groove weld using your corner and T joint geometry to be used in production however, then you are qualified for all groove details complying with 3.12 or 3.13, including T and corner joints, excluding square grooves, and within the limitations of Table 4.5 #33 if you move outside of the prequalified joint details.
For future reference, this is all based on the 2010 Edition.