In short, no. Word's bookmarks are ignored by FM's import filters (Reference is in the FM Filters.pdf manual last updated for FM7.2 in 2005).
You could possibly create a VBA macro in Word to extract the bookmarked content from the Word file(s) and place those into a MIF formatted file with each bookmarked snippet in a separate flow. Only then, could you import the individual bookmarks (as text insets). Maintenance issues are a consideration and your workflow would have to take into account how you would update the created file with new content and preserve the FM text insets.