Measuring spin on electrons prepared in various directions

Jeronimus
Let's say we have 200 electrons.

The first batch of 100 of those electrons are prepared in a way that 50% are UP in the x-axis while 50% are DOWN in the x direction. The order is unknown.

The second batch of 100 electrons are prepared in the same manner but in the y axis.

Bob picks one of the two batches randomly and sends it to a spin measuring device.

Alice runs the batch sent to her through the spin measuring device, and checks for the x spin of all 100 electrons.
Alice writes down the time interval it took for the device to figure out the spin for each of the electrons individually.

Then she does the same for the other batch.

Is it possible for Alice to figure out which of the two batches she was working with, simply by looking at the time intervals it took the machine to figure out the spin of each electron?

From what i read, a spin measuring device is basically a magnetic field you put the electron in, and which then has a certain probability to emit a photon or not to emit a photon within a given time-frame.
Does the average time-frame it takes depend on the initial alignment of the electron or is it the same no matter which direction the electron was prepared in?