The answer is yes..it is possible..There are many reasons why soil is not under normally consolidated condition.
a. Sampling and handling - unless you took the sample using sample freezing technique the disturbance due to sampling and handling is inevitable. It is almost impossible to sample soft to very soft clay without highly disturbing it.
b. Stress relieve - The sample experiences stress relieve when we took it from the depth, from whatever initial pressure was to zero (atmospheric pressure). Even if you took the sample using the sample freezing technique, you are still facing the disturbance due to stress relieve when the sample is thawed, which highly affects the pc' of your sample. When you did the Constant rate of consolidation (CRS) test, what you are actually measuring was the pc' when the sample was tested. Suzanne Lacasse and also others from NGI have discussed this in many of her/their papers. For example, Lunne et al -2006 - discussed this here: http://www.ingentaconnect.com/content/nrc/cgj/2006/00000043/00000007/art00006.