It works for me, with character and paragraph Styles alike. Indeed, you could even simplify the line to:
.Style = "DB_Content"

Do note that, apart from any paragraph-level attributes applied by your Style (e.g. alignment, space before/after, font name & size), hyperlinks have their own character Styles (basically, blue underlined text), so those will take precedence over your Style. You can, of course, re-apply the Style's font attributes such as bold & italics to the paragraph, so as to re-format the hyperlinks, after applying the Style, using code like:
before the 'End With'.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]