Yes, the time can depend significantly on the register. Here are a few examples (as measured on an Intel Core i7-8700K):
Here are the nanoBench commands I used for the measurements:
sudo ./kernel-nanoBench.sh -asm "rdmsr" -asm_init "mov RCX, 0xE8"
sudo ./kernel-nanoBench.sh -asm "rdmsr" -asm_init "mov RCX, 0x1A0"
sudo ./kernel-nanoBench.sh -asm "rdmsr" -asm_init "mov RCX, 0x19C"
sudo ./kernel-nanoBench.sh -asm "rdmsr" -asm_init "mov RCX, 0x198"
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