Homebrewing - Beer, Mead, Wine, Cider

I've given this a bit of thought from a chemical point of view. The issue here might not be just due to the amount of vegetal matter. I'd expect you to see this if you were to use extracts for the equivalent amount of alpha acids.

Just on a quick search, alpha acids seem to have a pKa (read lower for why this matters) of about 5-5.5 and a solubility in water of about 60 mg per liter at 100 C (and lower at room temps). source

Without going too much into chemistry, if your pH is lower than the pKa, you're more likely in this case to have less solubility (based on the ratio of ionized/molecular forms). Higher pH than pKa - more solubility. Same pH as pKa - about half and half.

Solubility would be helped by alcohol content though, but at 6.5% ABV you wouldn't see it going up that much. 14 g of a 10% AA hop would yield about 1.4 g alpha acids if my math is right.

(If you have the time and the disposition for such a test you could dilute some vodka to your ABV - about 100 mL should do it and add 1.4 g of your hops and see what it looks like. Then try different alcohol concentrations and see if you get any better results. You could also, for the hell of it proceed to pH adjust the mix and see if you get anything clear at a drinkable pH)

Solubility issues would present themselves as the well known haze. (for an extreme example see Ouzo + water) Removing it would also be slightly more difficult (even with filtration) and would probably have the side effect of removing the things you want in there.

Also, your water chemistry would influence said solubility - for example the amount of magnesium ions.

Note - all of this just takes into account alpha acids in water/alcohol. It becomes way more complex when thinking of all the other stuff present in beer. Which is to say that you may have a hard time obtaining a crystal clear beer with a huge amount of dry hopping.

TL;DR - chemistry wall of text; RDWHAHB