Unless the clear on your A3 is somehow different from that on all the (12+) Audis we've had, it's gonna be very hard. Sorry they messed it up so badly.
Assuming it's like the clear on my Audis, the #80 won't be enough to correct it and no, you won't run any real risk of making it worse.
The only way I can do correction on Audis with a PC is to use 4" pads. They're much more aggressive than the usual 6.5" pads that are so common. But you'll still need something more aggressive than the #80 to really get it nice.
Unfortunately the products I prefer are out of production and getting hard to find. Anyhow, they're 3M PI-III RC (05933) and PI-III MG (05937). Many passes with the 05933 and then a follow-up with the 05937.
In the absence of the above, I'd recommend you look into the polishes from 1Z, they're very user-friendly and IMO that's important as you're gonna have a big job ahead of you. Their Paint Polish might be aggressive enough, but you might even need their Extra Polish. Follow the Paint Polish with their MetallicPolishWax.
There are a lot of good choices you can use instead of the above, but I'd rather recommend stuff that I know (from first-hand experience) has worked well on Audis for me and others (including people who aren't really into detailing).
I wouldn't plan on using the Klasse twins or any other sealant approach. Just not likely that you'll get that black Audi paint as good as you'd need to for a sealant to look that good so I'd stick with a carnauba approach like the #16. It lasts a long time and you'll *love* the beading.
Sorry if the above sounds negative, but I've been dealing with Audi clear since the early '90s and it's quite a challenge.
Oh, and claying is advisable but not necessarily mandatory.
One other thought: if there's any chance the hood/bonnet was repainted that could change things drastically. If that was the case, I'd begin by having a serious discussion with the dealership.
Use it until you're tired of doing it and top with wax.