Hi Drecalps,
I was also an international student, after kong matapos ung program ko, I applied for PR through Alberta Provincial Nominee Paper Based nung January 2017, I received AOR in March, but no update till now.
However, nung maka-one year ako sa current employer ko nung September 2017 nagapply din ako ng Express Entry - Canadian Experience Class Stream (CEC). I just got PPR yesterday. It only took 3.5 months ung processing.
To answer your question, yes you can apply for both. But I suggest na magapply ka na lang ng Express Entry directly if you reach the minimum CRS kasi mas mabilis.
Kelan mo ba matatapos ung program mo?