C1 won't accept MyUS as an address so that is your first road block. I think they have their own address list that doesn't correspond to USPS's list.
Re fraud detection, I think it's always good to have your first card forwarded if possible to avoid being flagged. I also make an obligatory call to tell them that I'm travelling for work and expect charges etc and ask whether there are any issues.
For my first amex card, I had it forwarded to Anchorage as I was visiting so that probably put me in their good books since it was still within the US.
As a rule of thumb, best to keep a 'standard' profile with your initial relationship with the bank and don't raise too many eyebrows that would trigger fraud detection.
YMMV