"Android" is like... um, it's not the same thing as "Android" at all, depending on what devices people have. Android OS fragmentation is a real thing, and what browser people are using is a huge factor. :-/ So some Android devices will be perfectly great, others, not so much.
As far as an app goes - no, we wouldn't need a new server. Any app should be making calls to the same webserver webDip already runs on. It might maybe call a different page than the existing web users, but even that is not necessarily true, and certainly even if it did it wouldn't be a new server.
There *would* be some benefits to an app - having it show up in the iOS app store and/or Android Market would be good for advertising, no doubt. And having validation be all nice and app like, maybe even some sort of unit dragging interface, and all that sort of thing would be lovely. But it's a *lot* of code, and a lot of it duplicate to the existing web code, which could mean that fixes might need to be done in two places instead of one. Maintenance nightmare. :-/