Would there be any problems from accepting a title of nobility in a foreign country? I seem to recall a real life British officer was disparaged for accepting knighthood from a foreign country he aided.
...trying to sum up the issue in simple terms so I don't go on a long-winded rant.
Okay, so there are multiple facets to take into consideration when discussing something like this. One of those is whether or not the individual in question
already possesses a title or not.
If they don't, nobility is looked upon as a higher calling a 'mere' officer position in the armed forces. Even something as simple as a knighthood raises question of what a
commoner's first priority is going to be should they find themselves in a position of conflicting loyalties. Are they going to honor their oath of service to their superiors or will they decide that their future would be better following the path of a ruler who has raised their social status?
Because, not to put
too fine a point on it, but most nobility would do the latter, so even with the most loyal of commoner officers, possessing a foreign title of nobility, even one which is non-hereditary, is deeply suspicious.
Now, if the individual in question is already nobility, the question to ask is which title is higher? The domestic one or the foreign one? In Lelouch's case, he's a
prince. Not only that, but he's not actually part of the formal military structure. So not only does he generally
not have access to information in the empire's chain of command as a normal officer would, especially a high-ranking one, but he's also far more incentivized to see to his responsibilities as a prince than as a relatively low-ranked noble, so it's foolish to doubt his loyalty to the empire in light of that.
In other words, at Lelouch's rank, a foreign noble title of little stature is essentially an interesting bauble to brag about, but nothing which should really invite envy or suspicion. If Lelouch were to ever be elevated in the Chinese court to an equivalent position of Duke or adopted into the royal family...
then people will start to talk about divided loyalties.
So the answer to your question is dependent on context, a lot.