That should polish out. Polishing is an abrasive process that basically removes the outer layer of paint/clearcoat. This will tend to even out those small scratches (also known as swirl marks or "spiderwebbing") which you generally see only where the logo wasn't, and basically flatten out the surface so those small scratches basically disappear. It will also leave the polished surface looking very glossy, with deep reflections. Like if you have a sheet of water covering the surface.
You have basically two option for tackling this: either try to DIY, or take it to a car detailer to do it.
It is not rocket science to do it yourself, but there are some tools and materials to buy (and many more to pick from), and there is a learning curve to it. I'm sure there are a bunch of folks here who can help advise on products and technique if you wish to DIY, (since as you may know, many other of us Porsche owners also like to keep our cars looking good.
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I expect wax may also help (especially if you used a variety that has scratch filling capability, which perhaps the one you're using doesn't), but the effect would be temporary, so it's a "band-aid" solution. Polishing would be the
permanent scratch removing solution (and you can still wax or put a sealer over the top of the polished surface, too).
By the way, is that color lapis blue? I also have a lapis blue boxster - a 2001 - that is *very* badly swirled. I suspect it may be soft paint, or maybe just such a dark color the swirls are very noticeable (in certain lighting conditions at least). I've been wanting to polish it myself completely when I find the time. (So far, I've only polished one band across the front edge of the hood.
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