Yes, you could download all the needed .deb files and install them with dpkg. It's the same apt does, but apt resolves dependencies, and automatically downloads all needed files for you; if you do it manually, you're the one who has to make sure all the dependencies are downloaded. You could probably (if apt just supports it) ask apt to do a "fake" upgrade process, meaning that it would show what should be downloaded but wouldn't then do it. Sort of gave you a list of things to be downloaded. Then you could use that list as your "guide" when downloading them manually (they're on the Ubuntu reposities anyway, though it's not quite as easy getting them without apt doing it for you).
When you've downloaded the packages (put them into the same dir for easiness),
dpkg -i packagename.deb
for each package, or probably just
in the directory.
EDIT: you could probably also do
to have dpkg install (upgrade, if already installed) all the packages in /path/to/package/directory/ recursively; -R means "recursive", and with it you give dpkg the directory path under which all the packages to be installed are, rather than package names.
dpkg -Ri /path/to/package/directory/