Dombeaumont;
I believe that yes, you would have to wait in the UK to finish hours before being sent out to the states to start CPL, although if you are only a few hours short, then you may get sent out to finish the hours building in the US.
You won't be given a conditional offer based on a Class 1 medical. Likely your application will be removed at the paper sift stage in Leeds untill you have Class 1 in hand.
TTR