TSR is not as aggressive as a true compound. If you want to go after the deeper swirls and scratches then try a more aggressive compound. There's so many terms for products and no standard definitions that it's hard to say exactly what products like TSR are except to refer to them as polishes or cleaner/polishes or swirl mark removers.
The answer to your question is sort of no and sort of yes.
For everyone reading this into the future...
Removing swirls and scratches means removing a portion of the top layer of paint, this in effect levels the surface. In most cases here's what will happen, the shallow swirls and scratches will disappear. The scratches that remain are deeper and will stick out like a sore thumb BECAUSE the shallow zillions of lighter swirls and scratches that all over the surface acted to camouflage or mask the deeper scratches.
Make sense?
Now Spike's question is what will it take to remove the deeper scratches or the RIDS
RIDS = Random Isolated Deeper Scratches
RIDS - The Definition of RIDS and the story behind the term...
The answer is you can use a more aggressive product, you can use a more aggressive pad or both. You can also use a more aggressive tool depending upon what you're using up to this point.
Keep in mind that removing deeper scratches mean removing more paint so at some pint you need to make a value judgment as to how badly you want a show car finish or whether or not you can be happy with the results you've already achieved and live with the deeper defects that remain. If you car is a daily driver and you plan on keeping it for a long time then you might want to live with the deeper defects, if the car is a garage queen that you only drive occasionally and it deserves a finish worthy of it's marque, then continue working on the paint.