Connection Time – Foreign Locations

I am new to the VoIP world and am thinking on converting my home based business over. I apologize in advance for what might be simple questions. I travel frequently for work/pleasure, and am entertaining the idea of working from a foreign location for 3-6 months/year. Question 1) When someone calls your phone number (US area Code), if one is connected to a strong broadband signal say in Paris, is there a noticeable delay before the connection is made to my computer/phone in a distant location? I am afraid that if there is a long delay before connection, I may lose the caller. 2) If the computer/phone is shut off, will the phone call automatically be routed to voice mail?