Some shocks use a LSC metering method to control pedal bob, others use a platform. Some, like the new Fox DPS (I believe) use both depending on whether you’re in open or trail.
The tune of a shock normally relates to the shim stack, which is controlling the high speed damping, so no, the higher damped shock shouldn’t offer more pedal bob resistance than the low tune if its a platform type shock. As an example the Monarch RT/RT3 shocks have a factory set platform resistance that would be the same for any compression tune (assuming that is how it was specced – there are choices in terms of platform stiffness).
That said, High Speed is a bit of a miss leading term, as high speed is not necessarily all that high speed. In a typical shim stack even moderate pedal input will cause the stack to begin to deform, so the stack is contributing to the anti-bob of the shock, and so conversely the answer is also yes, high compression tunes will effect the anti-bob of a shock, but its not so clear cut as to say that a low/low has less anti-bob than a high/high – its probably not designed to, but it might be an additional effect of the tune.