Using the definite article with abbreviations

Hello,

Could you please say whether it is necessary to use the definite article with an abbreviation if the corresponding non-abbreviated expression requires the article? For example, if a name "the University of California" requires the definite article, should we use the article in the abbreviation "the? UC"?

The topic seems somewhat controversial because most people within universities named "University of {Something}" do not use the definite article before the abbreviated names of their universities, but almost always English speakers use the definite article before the abbreviation "US".

One opinion stated in The Chicago Manual of Style is that initialisms, such as "UC" or "US", are usually preceded by an article, while acronyms, such as "NATO", almost never are. Due to the presense of "usually" and "almost never" in this description, I would not mind having other opinions. Maybe there is some rule of the thumb or a common practice of using the definite article with abbreviations?

Thank you.

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Victor