Sure, you can force a fiction of O(1) by dramatically increasing latency and strictly limiting the size of memory, as we do with microcontrollers. This would now be O(1) with a very large constant factor overhead, basically pinning memory access to the latency of the memory cells that are furthest from the CPU.
I'm not disputing you can establish an upper bound on latency. You can always do this by using a system's slowest component as the upper bound and pin everything else's latency to that bound, as I said. I'm just pointing out that this upper bound a) doesn't scale well/leaves a lot of performance on the floor, and b) the upper bound is very sensitive to size and geometry.
In high performance systems, constant time random access is just not constant.