No the fronts won't fit, you need 5.25" components or 4" for the fronts with a max depth of 60mm. The main problem in the A3/S3 is the lack of bass and you won't solve that issue by upgrading speakers. Your money is best spent on a stealth sub or proper sub, then you can run the HU at a minus Bass setting which will dramatically improve the sound from the front components. The rears are a waste of time TBH unless you have passengers in the back a lot.
Also bear in mind how the new HU will be wired. If you are gonna run the rears off the HU amp and bypass the Audi amp, then you still need to feed the rear amp otherwise you'll lose the sub as well. Even if you retain the existing sub it will sound even more feeble than it does at the moment as you have doubled the power to the cabin speakers but left the sub at it's original 50watts. So at the same volume level the sub will be quieter unless you wire it up to the sub out of the Kenwood (if it has one) and then jack up the sub level to compensate.
I've installed my stealth sub for customers who'd already speant over £1k trying to improve the sound with expensive HU/speaker upgrades and the results aren't good. They were giving the sub a go as a last resort and couldn't believe the difference it makes. It doesn't provide overpowering bumper rattling bass, just nice tight punchy bass and allows you to run the cabin speakers much harder without distortion.
TBH I did exactly the same thing in our A3, started with upgrading the speakers, little improvement, added a new Alpine HU, then an Amp, and lastly a 10" Apline sub. It was the sub that had the biggest "bang for buck". With a family on the way we needed the boot space back so I started experimenting with the standard sub as I just could not live with the feeble downgrade of losing the proper sub. Once I'd got the stealth sub installed the sound was superb and it wasn't until I fitted another one to my mates A3TQ with everything else left standard that I realised the great sound was 90% down to the sub on its own and the speaker & HU upgrades had really very little effect apart from the benefit of sub control (which you don't get on the OEM HU).