The situation is a bit similar to driving up hill on a bumpy road.
The car's suspension definitely transfers the "average force" from the road up to the passengers, but let's talk about what "average force means.
There's no good way to do this without talking about high frequency, low frequency and DC/constant.
If the road were a perfectly smooth inclined ramp, the force would be DC and the vertical climb velocity of the passenger would be the same as the wheels.
If the road were rough with lots of little bumps, then the wheels would go up and down but the passenger wouldn't (if the suspension was good).
But if the road now had a lot of dips, say 50 cm deep and a few meters long, then the suspension couldn't respond fully to that and the car and passenger would dip right along with the wheels.
So the suspension of the car or the vibration isolation system for the rocket payload will absorb a lot of the high frequency stuff but start passing more and more of the low frequency stuff and all of the zero frequency stuff.
The rocket and the payload will get to space at the same time, but they will experience the bumps and dips differently.