Just got my response (a lot quicker than I would've thought at this time of the night)
Thank you for contacting Newegg.
We apologize for any inconvenience this may caused. Actually, Newegg.ca cannot redeem the gift card purchased on Newgg.com. Thank you for your understanding.
If you have any further questions or concerns, please visit our FAQs page. If you still require any assistance, please feel free to reply directly to this email.
So apparently it won't.... who'd have thought. I have asked an additional question - whether or not I can buy a Newegg.ca gift card since I don't live in Canada. It'd asked me what Province I lived in and since I don't live there... well I can't really answer that.