There is no way to update the pages with bilingual content until you publish the bilingual theme. If you do, you'll see *both* languages on your existing theme, until you switch to the Bilingual THeme This is because other themes don't understand the bilingual switch.
However, there is a way around it.
You can re-create the pages with BOTH languages, as a new page. Then, when you're ready to publish, you can just change the links under navigation, to point to the new pages.
For example, let's say you have an "About Us" page in English right now. Let's pretend you want to add a Danish version when you switch to the Bilingual Theme.
Because other themes won't understand bilingual setup, we don't want to add English and Danish to your existing "About Us" page.
What you can do is go to Admin > Pages, and create a new About Us Page. For example you could call it "About Us - New". No one will see this page, because it's not linked from your navigation yet. You can then enter your content in BOTH English and Danish on this new page.
When you publish the new theme (bilingual), go to Admin > Navigation, and change the link to "About Us" pointing from your current page (English only) to your new page (both languages). This switch will take you about 10 seconds.
Repeat for other pages as needed.