Hey chendawg--
Visiting campus before applying is ALWAYS a good strategy -- it's one of the best ways to decide if the school is right for you, for exactly the reasons you've cited. Experiecing a school's culture firsthand is really important - many people think schools are interchangeable, and they're just not. We think it's the best way to figure out whether to even apply (we talk about it on our blog quite a bit - here's a few posts:
https://essaysnark.blocked/2010/06/ ... chool.html and
https://essaysnark.blocked/2011/04/school-fit.html ) AND it also can give you important insights that you can use in your app. So it's a huge advantage for the candidate, both in deciding if it's the right school for him, and then in better articulating the reasons why when developing the essays.
For schools like Owen that have these candidate-initiated interviews, no, they certainly don't expect that you'd have your application complete before you go to campus. Few people do. In fact, some schools with this interview-in-advance policy (Tuck comes to mind) specifically offer the opportunity as a way to weed out those who discover that the school isn't the right place for them. This is certainly one of the (many) reasons behind the Owen policy, too. They say it directly on their website - they want people to come find out what "Owen, Vanderbilt, and Nashville" is all about. They want to make sure that those who do apply are really in love with the place. So, offering these pre-app interviews is a win-win for everyone.
You probably should take preliminary steps towards starting your app, just in case it comes up - they won't expect that you have finished it, given how far off the next deadline is, but it would be good to have a minimally positive answer, right?

However, we sincerely doubt this is going to come up. It doesn't really matter, from their perspective - you're showing great interest by making the effort to trek all the way to TN, so you've already crossed a major hurdle, in their eyes. They will be evaluating you based on how you present yourself to them (background, career goals, why Owen), not how far along you are in your application.
The main reason you might want to go through their online app in detail before heading to campus is that if they have any oddball questions in the app, you could get clarification on it directly with the admissions office. Some schools ask questions that are puzzling. Can't recall offhand if Owen has anything in that category, but getting familiar with all of it now could save you some time later.
Campus visits tend to be FUN - it's usually really energizing to be around all those smart people who are learning really cool stuff. So, do some prep now as you're doing - but then relax and enjoy it!! It's only going to help you in all aspects of your process (even if you were to decide that Owen isn't the right school for you, you will likely learn SO MUCH that you can use in your other apps that it'll be a net gain).
Good luck!
EssaySnark