Do my squad mate's outfits affect their stats?

mass-effect-3

Yes they do. 

          Default        Alternate       N7 Pack       AshesDLC  
EDI        PD              PRS            n/a          Shields   
Javik      PD              PRS            n/a           n/a  
Liara      PD              PRS            PD            PRS  
Garrus   Shields            WD            n/a            WD  
James    Shields            WD          Shields          WD  
Ashely   Shields            WD           PRS             WD
Kaidan    PRS               PD            WD           Shields
Tali       PD              PRS            n/a            WD

All bumps are +25%, PD=Power Damage, WD=Weapon Damage, PRS=Power Recharge Speed.

Values are summarized from the wiki.

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