You will not see any of your european friends if they are not attending the D3 Open Beta. I've sent an invitation to someone that is playing D3 - Worked. Sending it to someone who is just playing WoW on an european server - did not work.
If you're on an EU server and want to add someone from a US server, are you able to do that? Or can you only chat and add people from your servers?
I'd have thought, given how servers seem to work, that EU can only add EU, and US can only add US, but I've not found anything anywhere that confirms or denies it, so I thought I'd ask.