Why one time would not suffice to collect data?
It is acceptable by design to pass through / cross 1st critical speed during start up, otherwise the compressor will never start.
There is not only the critical speed value to look at, but also separation margins, amplification factor which are covered by API 617 if your machine is to this standard.
If the machine does not trip during normal start up then there is no reason why it would be prevented to start during the test procedure you intend to put in place unless you are not operating in "chartered area". Refer also to MRT procedure and vibration readings based on OEM manual as there are incremental steps for ramp up and run down, oil temperature stabilization etc.