As Nat notes, this is possible.
If you instead click the 6th button on the bar, the effect will REPLACE all effects in selected clips.
To apply a global effect after completing all the individual clip editing.
1) Open a new blank sequence by clicking the + sign at the right of the Sequence 1 tab, above the thumbnails.
2) Click the Sequences tab above the clip bin (top-left) and right-click on the Sequence 1 folder.
3) Click PLACE CLIP ON SEQUENCE. (Or simply drag Sequence 1 onto Sequence 2.)
This is now a single clip of your entire project. The overlays and audio won't be seen on the sequence, they are all there.
Apply the global effect, then export. If later changes are needed, go back to Sequence 1, make them, then redo the steps above.