If not then what of Zhodani noble's offspring? They are born as proles.
Not quite. Check the Psionics section of
LBB:3. Everyone has a psionic potential as rolled on 2D6, a potential which begins to degrade after age 18 if it is not identified and the individual trained. The children of Zho nobles will be tested and trained as soon as possible.
The real trouble begins when a noble's child has a psionic strength of 2...
Look at page 12 of
CT's AM:4 Zhodani for a quick primer on Zho society, specifically under
Ambition in the
Psychology section. While ambition in Zho society is neatly explained, ambition for social advancement is said to explicitly rely on psionic strength. An explanation of social advancement for all three part of Zho society is then given.
Prole children can elevated into the Intendant class if they exhibit the required psionic strength. Further answering your question,
AM:4 states
... Because Psionic strength is not inherited (it seems the be random within the population), ... So, a prole child with a marked psionic potential is going to become an Intendant.
Indendants then become nobles be competing within the Psionic Games at a rate of about 1 in 7 or as a reward for service at a rate of about 2 in 7. The social standing of children of an indendant will depend on their psionic strength too.
Nobles then advance in a manner similar to Imperial nobles. Noble children, like all children, will have some psionic strength. One child will inherit the title, perhaps due to their psionic strength or perhaps regardless of the same. (Non-inheriting titles presumably "devolve" in the usual manner; i.e. Churchill being a gentleman, his non-inheriting father a "mere" Lord, and his grandfather a Duke.)
Very intriguingly,
AM:4 talks about "discouraged" nobles including
"Some hereditary Nobles have low Psionic Strengths and (even though they have psionic training) their abilities are low."
I've always thought these "low psi" and (perhaps) non-inheriting Zho nobles are an overlooked pat of the Consulate, an overlooked and very intriguing part of the Consulate. There will be prejudice against them, nothing overt but certainly institutional. They're going to be assigned "hi psi" indendants both as a crutch and quite possibly as a way of keeping an eye on them. Finally, these "low psi" nobles are going to be "sandboxed" when at all possible, shunted aside into positions and duties which aren't seen as important.
Any GM worth his Cheetos can see the opportunities presented by "low psi" Zho nobles.
IMTU I am leaning towards no, thus the nobility is meritocratic and highly infused with the sufi-istic mysticism of the nobility. It would almost be relief to be born as prole in many ways, not to be caught up in the hidebound monkish ways of the nobility.
I think that's a rather interesting way of describing the situation and one which could only help but add to the texture of your
TU.
On the subject of psi being inherited, I believe there is some color text in
MT repeating the
CT line about psi strength being random in the population and also suggesting there may be a slight environmental component. ISTR, something along the lines of being raised in a psionic household providing a statistical "blip" to someone's initial psionic strength.