Not built in, no. But you could do this:
Create a new paragraph style called "Delete Me". In the paragraph styles
palette, select all the paragraph styles you're NOT interested in.
Delete them in one go, and replace them with "Delete Me."
Now, in the find/replace box, search for "Delete Me" and replace with
nothing. This will cause all the paragraphs that have the "Delete Me"
style to be deleted.
Now what remains in your document is only the text that you're
I do stuff like this all the time. I find it easier to use TextStitch to ensure that the whole document is one long story, then export that story to RTF, open that RTF in Word, use "Find All In Document" to select only-text-in-one-style, then copy and paste that selection into a new doc.
I hate to say it, but this is one of those cases where selection of multiple non-contiguous chunks of text (i.e. "that thing that MS Word can do that InDesign can't") is really worthwhile.