No need for a master frame. Just create an object style for a text frame and set it as the default.
Place the text. Done.
is there a way to pre-apply a style to that frame across all 200 pages
What Bob said, but if you want to use the master frame you can select it and assign the style, or put the cursor in it and assign the style. Keep in mind, though, that doesn't guarantee the style will be honored when pasting text. That depends on your settings in the prefs for what you choose to paste or if you choose paste without formatting. If you've elected to paste styles, and you paste formatted text, the incoming formatting is going to override the applied style and be preserved.
Thanks. Here is a more detailed question :
I am specifically pasting in two lines of text. Can I set the object style to treat the two lines differently? I know that you can normally set "Next line" in a style, so once you hit enter it will go to the next style. But would it work when pasting two lines?
I tried setting an object style to use next style, than pasted in several paragraphs using paste without formatting. The pasted text all used the first style, but the next style did trigger correctly when I hit the Enter key, which is no help here.