Maybe you'll lose weight, and maybe not. It depends on how much you eat. A tour isn't a great time to lose weight, however, since you'll need all the energy you can get. I would say not to try to or count on weight loss on tour. If it happens, it happens.
Yes, you'd have to leave earlier to compensate.
How long it takes before you can ride 60 miles a day depends on what kind of shape you're in before you start. And it's not just leg shape, but butt hardening, neck and back conditioning, etc. A young, fit person can probably start from scratch and be riding 60 miles a day within a couple of weeks. An older, out-of-shape person may not get to that level for months. My advice is to get into as good a shape as your schedule permits before you start, but go regardless. If you have a rigid end date, then just go home from wherever you are on that date, even if you didn't make it as far as you hoped.
Success rate has a strong correlation to attitude. If you have plenty of time and plenty of determination, and don't push yourself so hard that you get saddle sores or muscles injuries, then you'll make it. If you're not having fun or push yourself into trouble, you won't. Somebody told me that the chances of a solo tourer completing the TransAm is only 50%, but goes up to 95% if you can get through the first 10 days.
Not touching a bike until the day your tour started would probably be a recipe for failure unless you are very smart and very determined and very lucky.