I am not sure what effect if any a 32 bit vs 64 bit architecture processor has on disk read/write speed.
I believe that a 64 bit processor can address more main memory than 32 bit processor without TLB cache, but does it affect the read/write speed of an hdd?
Processor architecture does not inherently affect disk I/O speeds, nor does it affect memory access speed. Generally speaking, it only affects the amount of memory that the system can use. Disk I/O speed is determined primarily by the physical properties of the hard drive or SSD itself.
It depends on the program, how much data you're writing (cache size), and the speed of the storage relative to the data you're writing. For example, if I have a trivial program that adds an infinite amount of 64-bit integers together, it's clear that the program will run faster if compiled to take advantage of a 64-bit processor (instead of using the 32-bit counterpart instructions). However, the work done is trivial, and the CPU can add numbers together much faster than you can store them onto an HDD/SSD (thus filling up the cache on the disk drive, limiting the operation to the storage speed).
However, if we look at the operations done by the CPU, we can see that the 32-bit version will take longer to complete, only performing work and copying 32 bits of memory at a time to the cache controller (with the use of direct memory access (DMA)). In this case, the 64-bit operation might theoretically fill the disk's cache controller more quickly for burst operations, it's more likely that in both cases, the cache would be filled and the operation speed would be limited mostly by the write speed of the disk itself.
