Not a developer here, but yes. that is one of the fundamental attractions of concrete5, that you can "concretize" an existing html design. The biggest caveat to that probably is with JavaScript, since concrete5 already implements JavaScript into its core functions. So it may depend on how your site is built and what kind of js or other dynamic elements you already have. Here are a couple of threads to review. These are older posts, but hopefully they'll give you an idea of what's involved.

http://www.concrete5.org/documentation/how-tos/designers/make-a-the...

http://www.concrete5.org/documentation/how-tos/designers/converting...

http://www.codeblog.ch/2009/01/concrete5-theme-erstellen/...

I agree with @brandsmarter's answer -- but note that doing this is a fairly decent amount of work. There is no way to just automatically convert an existing HTML site into a Concrete5 site -- it requires that you take your HTML and construct a Concrete5 theme out of it. This is true for all the major CMS's (wordpress, drupal, joomla, etc.).
If you don't want to go through this trouble, you might want to try "Perch" (http://grabaperch.com/ ), which is a very simple CMS that *is* easy to drop into an existing HTML site -- but the downside is that its feature set is very limited compared to Concrete5 (but it might be enough features for you, so I'd check it out and see).

This is not something I have done, but my interpretation of the C5 .htaccess suggests that if you have a static html page in the same web space as a C5 site that html will be served in preference (please do experiments to check before relying on this).

In particular, .htaccess tests to see if any http request maps to an existing file and simply serves the file, whether it is a picture, script, or html page. Only if the file does not exists does the C5 dispatcher get called.

With that in mind, I suspect you will need to move the home page into C5. The rest could coexist within the same web space, though you may have to install C5 into a subdirectory if any of the directory or filenames clash.

The rest is as previously noted, creating a C5 theme matches your co-existing html theme. For links between the two, in C5 you can code them as external links.

I don't think this answer applies to the question -- I'm pretty sure the OP is asking how to make the existing HTML site editable with a CMS, not just how to have both a CMS site and the static HTML site exist as separate entities on the same server.