you're right, I meant $0000 and $0001 which _are_ registers. The rest 254, yeah. Zeropage is a must on C64 at least. I don't know much about other platforms.
So 0 and 1 are connected to the 6510 I/O data direction and I/O data register, but there is still RAM there too. Seems the 6510 won't issue write signals to the bus for addresses 0 and 1, but the VIC can see them and it's readable through sprite collisions.
They're not physically connected, other than through the bus. I mean, zero page is part of DRAM.