There's a couple of issues that spring to mind immediately. First, the key missing element is alternate shot and without that there goes Day 1 and 8 points worth of matches. We could easily do the fourball and singles matches without a problem. We just need something else to replace alternate shot.
Second is the amount of international players. You need 12 to form a team. Can you find 12 international players who can compete with the top of the American crop?
Scheduling is the third issue. You will most likely always be playing against someone at least a few time zones away, but that's the least of the concerns and can be problaby be remedied. I'm also concerned about lag between distant connections.
If we can clear the hurdles of #1 and #2, then no, I don't see why we couldn't do this eventually.