Last week I did A11S with a random party.

The short answer is "yes" you can clear even the hardest dungeons with a random party.

However, the long answer is that there is no way you will clear that unless each person in that party knows exactly what to do, when to do it, and has practiced for many hours.
It took me 3 weeks of practice every day before I could clear Alexander floor 11 Savage. But now, it's easy for me.

The reason even random parties can clear it is that most parties will follow the same strategy to do it, with some minor adjustments depending on server / datacenter.
This is why, at the beginning of the fight, a tank will usually run a macro explaining the recommended fight mechanics. If everyone can follow them perfectly, it can be cleared.