Question

Is it true that nucleus of unicellular organisms may not be fully developed?

Answer 1

In an unicellular organism there is only one cell which is either completely developed or not developed. 
Development of nucleus depends on whether an organism is eukaryotic or prokaryotic
Eukaryotic unicellular organisms are having completely developed nucleus whereas prokaryotes do not.

Answer 2

if the unicellular organism is eukaryotic then the nucleus of that organism is developed..
if the organism is prokaryotic then the nucleus is not developed.