The 6510(6502 plus IO-ports) could do no such thing. Fastest instructions used 2 cycles and 1 byte op-code.
For example the instructions NOP(or CLI, STI, INX etc), 1 byte, 2 cycles. 1 cycle for fetching the instruction and one for executing the fetched instruction.
LDA addr,x seems to be pipelined a bit though. It's "AD lo hi" in memory and takes 4 cycles unless lo+x > 255, then it takes 5 cycles. The lo+x calculation seems to occur while hi is being read.
I am restoring a 65c02-based //e clone, so, I may be able to properly measure instruction timings, but I won't hold my breath.
Sounds like a fun project.