The Hold Button

Say the text you want to append to the file is in two separate parts. Copy the first part. Launch Take Note. Now, click the Hold button. Take Note will remember the first part of the text while you return to your original application to get the second part. Copy the second part of the text, then return to Take Note. Take Note adds the second part of the text to the text it remembers from before. Now you can click the Append button and append all the text to your file.

Take Note will automatically bring the original application back to the front for you when you click the Hold or Append button. 

That is, say you're in Word, and you launch Take Note from the Apple Menu, or with a QuicKey. When you exit Take Note using the Hold or Append button, Word will automatically come back to the front.

Of course, if you launch Take Note from the Finder, it will return to the Finder when you press the Hold or Append button.

If you return to Take Note without changing what's in the clipboard, the text will not be re-appended. Take Note checks, so that you won't accidentally get two copies of the same text.