V CE in the emitter follower configuration
Absolutely not! Vce is whatever it needs to be, in order that the emitter remains Vbe below the base.

One use for the emitter follower is as a buffer, to isolate lhe load on the emitter from whatever voltage is present on the collector.

So with Vin=5.7V, Vout will be (approximately) 5V whether Vc is 6V, 12V, or 100V (given a suitable transistor), and Vce would be 1V, 7V or 95V in these cases.

Of course, if the collector voltage falls below 5.2V in this example, it no longer works (drawing the emitter current from Vin instead).