Yes, all 64kb of RAM is accessible. But you ask an interesting question, if we change one letter. ; - )
Address space and device mapping
You asked about RAM, but how is RAM read? The CPU puts a 16-bit address on the address bus, puts the R/W' line in the desired state, and then expects a value on the 8-bit data bus within a certain time. What sends the data that comes back? Something else connected to these shared buses and configured to respond to the given address. It might be onboard RAM, ROM, a peripheral card, or something else. (I will document a few anomalies below.)
The point being that because the buses are shared, the 16-bit address space is shared, and parts claimed by various devices according to physical (cards etc) and logical (soft-switch) configuration.
On the original Apple II or II+ there is up to 48kb on the motherboard. The extra 16kb (or more) of the "RAM device" decoding is split between the motherboard and a RAM (e.g. Language) Card.
A 64kb Apple //e is very similar to the II+ with LC, except that the entire 64kb is onboard. In fact in the //e, $DXXX accesses to LC Bank 1 are converted to "physical RAM device" addresses in $CXXX. (For details see Sather's Understanding the Apple //e, page 5-24, third paragraph.) If a //e has 128kb or more then the Auxiliary Slot again divides the RAM "device" decoding.
In most Apple IIs $CXXX only accesses peripheral card RAM (or card ROM etc) and onboard ROM, but the //c+ has has 2k of "secret" RAM accessed through a $20 byte window at $CE00.
If you replace the RAM in your question with ROM (one letter, as I said) the question becomes more interesting, and you have in fact suggested a good place to look: $C0XX. This address space is always claimed by the softswitch decoding logic, and yet both the Apple //e and //c have ROMs called CD, EF or CF that are large enough to fully occupy $C000 to $FFFF. And in fact they do. You cannot read the $C0XX ROM area from inside the Apple, but if you dump any //c ROM (not //c+) and look at the beginning where $C000 to $C0FF would be, you find this:
Peter Quinn, Rick Rice, Joe Ennis, J MacDougall, Ken Victor, E
Beernink, JR Huston, RC Williams, S DesJardin, Randy Bleske, Rob
Gemmell, Stan Robbins, Donna Keyes, Doug Farrar, Rich Jordan, Jerry
Devlin, John Medica, B Etheredge, Dave Downey, Conrad Rogers
Hidden in this inaccessible $C0XX ROM are the names of the creators of the //c.
What if no device claims an address read? The Apple II was architected such that the CPU accesses the buses during one of its internal phases, and the video scanner uses the other phase to read video data from RAM to generate video. Bob Bishop discovered in 1982 that reads at unclaimed addresses return the most recently scanned video data. Examples are softswitches that do not return data, and vacant slot memory in $CXXX. A few games used this "floating bus" data to sync their graphics page-flipping with monitor refresh to avoid flicker. The technique is sometimes referred to as "vapor lock".