I think it is going to depend on the version of Microsoft Word. Older versions of Word (before 2007) will require some COM interop, because they are not saved in an open format. Nothing you can do to get around that, and I feel your frustrations with installing anything Office on a web server. Additionally, I believe the only way to detect password protection on these is to attempt to open/unprotect the file and catch a certain exception (you may have to further evaluate an error code within the exception as well). Not pretty!
However, for newer versions of word (2007+) saved in the open DOCX format (Standard ECMA-376), you can examine the XML and check for the existence of the DocumentProtection
element with the w:enforcement
attribute set to "on"...
<w:DocumentProtection
w:edit="read-only"
w:enforcement="on"
w:unprotectPassword="1FC6CBEB"/>
Note: The password seen here is encrypted (obviously); I saved this particular document with a password of "test".