The short answer is 'Yes, you can move your existing site to SilverStripe.'

I'm in the middle of doing just that. A few notes from my experiences so far:

Do the first couple of tutorials - they will give you a good feel for how it all works.

You will be building everything inside the 'mysite' folder, replacing its contents with your (modified) current files.

I moved out my text formatting CSS to a separate stylesheet called typography.css and added a typography class to the content wrapper div in my template. This means the CMS admin page can reference the styles. Have a look at the typography.css in the tutorial and the tutorial page.ss template.

As a first pass, you can just insert $content to replace your current text to create basic templates.

The next stage is reworking the menus so they are generated automatically from the structure rather than hand-built. That will be fun but the forums have lots of examples, eg how to feed data into existing pop-up menus.

Then you start writing the list of all the new possibilities that never existed while you had a static site!

cheers
bruce