International Roaming & Rejecting Incoming Calls

Yes to both questions. If you get a lot of incoming calls that you don't want to receive while you are abroad*, the best way to handle it is to forward all your incoming calls to voicemail (i.e. Unconditional Call Forward). In Free Data Roaming countries you can check your Visual Voicemail for free (I think). You can text your reply or wait until you're in WiFi coverage to call. I'd also, change my voicemail greeting requesting that people text or e-mail you, rather than leaving voicemail. There's a recent thread on this subject. Overseas Travel: How can I avoid incoming call costs but still use free text/data roaming while abroad?

*Imagine you're in Japan where there's a 13 hour time difference, someone calls you at 2:00 pm in the US, but your phone rings at 3 am in Japan.