There can be quite a bit of water in the oil and it still will lubricate. As long as it is not run for a long period of time or under heavy load, I don't think that will hurt much. As I said there was LOTS of water in my oil and that engine has gone about 80,000 miles since then and uses NO oil.
Yes, I think you can get it back together in an eight hour day. Given the oil situation though make sure you go through several cycles of oil change with cheap oil and filter, then put in a premium filter and your favorite oil for the trip.
I would make hard, firm plans for that trip though because you never know what you're going to run into. You might end up needing a part, or something. Don't take any chances or cut any corners just so you can make your trip. Doing that would be short term thinking with long term consequences.