As Marcus Muller noted, nothing requires the power to be equal to 1. (1 in what units?) It's nothing more than a convenience commonly used in textbooks and papers to simplify the math.
In general, if the signal includes a preamble, its power is likely to be the same as that of the information-bearing symbols. One reason for this is that if there is an automatic gain control (AGC) loop in the system, it can be confused by the time-varying power that having a preamble with a different power level would cause. Another reason is that the same factors that drive you to choose the transmit power of the information-bearing symbols also constrain the power of the preamble. You usually want to transmit as much power as you can subject to power consumption limits, thermal considerations, hardware capabilities, interference considerations, etc.
With that said, everything depends on the circumstances and there are no hard "musts." There could be some situations in which a preamble should have a different power level. It's just not typical.