#xbox360 help

So here's the deal

I have a really old Arcade Xbox360 that can't connect to the internet and Xbox Live.

I have a profile on this Xbox that also has never been used on Xbox Live.

On Christmas I'll be getting a new Xbox360 slim, and so here's the question.

When I transfer the profile and other content from my old Xbox to my new one, will I be able to connect that old profile to Xbox Live at all?

I've tried googling this question but it's apparently too specific or something because I can't find a clear answer.