In the x86 architecture you can't tell a physical address from a virtual address by just looking at the address value.
In your example1, 0x123456789 is just an address.
If paging is enabled then every memory access performed by the program uses a virtual address.
If paging is not enabled then the address used is physical2.
However since all major OSes uses paging, every program uses virtual addresses.
So is there a CPU virtual address space independent of the operating system?
The CPU is a general purpose chip, it just offers features to the running software.
The OS can use them or not, the CPU won't give any use any special meaning.
It's like asking if the a postal system is independent of the senders/recipients.
Yes, it is independent in the sense that it doesn't particularly care about whom mails whom but it is the senders/recipients that make the system useful/alive.
So it is the OS that uses the translation feature offered by the CPU, anyway it wants.
Why would this be needed in addition to the kernel virtual address space?
I don't know what is a "kernel virtual address space" in this context but in general an OS cannot track all memory accesses performed by a program.
So it need hardware support (read: a specific CPU feature. read: paging) to translate their accesses.
How would the CPU even perform a virtual to physical translation without an operating system?
The same way it would perform an addition, an IO or any other operation: it fetches instructions, execute them and change its states (including the translation map from virtual to physical) based on their result/behavior.
Being these instructions the result of the compilation of an OS kernel, a JTAG debugger or cosmic rays heavy rain, little matters.
1 In your example is EBX
that must be 0x123456789.
2 Note that a virtual address can be a logical address (selector:offset) or a linear address (after being transformed). Without paging the term "physical address" is not actually used, instead an address is simply logical (segment:offset) or linear. In the context above "physical" means "won't undergo an MMU translation".