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So I am about to get a GTS LMIA. So that would be a new work permit that would not be tied to her. The principal foreign national rule shouldn't apply right? She should be able to get a work permit correct?

Assume you mean the employer is getting the LMIA. Would warn you that the advertised short processing time can take much longer than that although some do get a WP in around 3 weeks but we typically see WP taking 1-3+ months. Still much faster than standard WP. WPs are not guaranteed so impossible to comment. If you your spouse become inadmissible then she would have to leave Canada to be able to apply for SOWP. Is your spouse actively studying full-time at the moment and is the school ok with this?
 
Assume you mean the employer is getting the LMIA. Would warn you that the advertised short processing time can take much longer than that although some do get a WP in around 3 weeks but we typically see WP taking 1-3+ months. Still much faster than standard WP. WPs are not guaranteed so impossible to comment. If you your spouse become inadmissible then she would have to leave Canada to be able to apply for SOWP. Is your spouse actively studying full-time at the moment and is the school ok with this?

So to confirm, if I get the WP successfully she should be able to convert since it is not based on my SOWP but rather a separate closed work permit? She is studying full time. Is the school okay with what specifically.