Well, we now have 4 members with quartered arms.
I'm really not 100% sure why they say they'll deny them, other than the fact that they're HIGHLY popular. Quartering is often also used in marshaling (combining separate arms into new arms), so they may be trying to reserve it for that.
In the long run I think all that matters is whether YOU are happy with your chosen arms. Registering them in various places just helps you to protect your uniqueness against other folks making the same thing (if they care to register as well, otherwise they'll never know it's in use).
The US Heraldry site Sir Brian posted is an attempt at creating a US-based college of heraldry, since we don't have any government sanctioned equivalent. It appears to be run by the Mormons out in Utah, which isn't too surprising since they're super-huge fans of genealogy and the like.
Registering with the SCA covers the big, huge 800 lb Gorilla of the historical enthusiast community.
To me the latter was useful, since I want to be able to display my arms when I go to Pennsic, and to be able to truthfully say "Yes, those are my registered arms". If you don't have it registered, then they could ask you to put it away if it too closely resembles someone else's arms. If it doesn't, no one will likely notice or care whether or not it's registered.
So basically, I'll encourage you guys to register your arms far and wide if you want, but what we establish in the Order really only matters to the Order, in the grand scheme of things.