Yes, you can absolutely install directly from your own website. If you point your browser at the URL where your package is, it will know how to install it upon download.
As for updates, I don't believe you could have it do updates automatically when they're available without some other mechanism (having the app call home and check for updates or something), but if you just point the browser at the updated package to download it, it will handle the upgrade as well upon download and installation.
