Learn English – Capitalization of a word after an ellipsis

First, some definitions from the Chicago Manual of Style:

• acronym refers to terms based on the initial letters of their various elements and read as single words (AIDS, laser, NASA, scuba);
• initialism refers to terms read as a series of letters (AOL, NBA, XML);
• contraction refers to abbreviations that include the first and last letters of the full word (Mr., amt.).

As for the capitalization of these constructs, CMS has these recommendations:

Initialisms tend to appear in all capital letters, even when they are not derived from proper nouns (HIV, VP, LCD). With frequent use, however, acronyms—especially those of five or more letters—will sometimes become lowercase (scuba); those that are derived from proper nouns retain an initial capital. Chicago generally prefers the all-capital form, unless the term is listed otherwise in Webster’s. [NAFTA (not Nafta)]

On the other hand, if the words in a spelled-out version of an acronym or initialism are not derived from proper nouns or do not themselves constitute a proper noun (as in the official name of an organization), they should generally be lowercased, even when they appear alongside the abbreviated form. [transmission-control protocol/Internet protocol (TCP/IP)]

So, whether CAOWS is:

• an acronym, pronounced cows
• an initialism, pronounced "SEE-AY-OH-DUBYA-ESS"

the Chicago Manual, at least, would recommend you write:

My coworker Steve suffers from Complete Avoidance of Work Syndrome (CAOWS).

Note that in Nathan's comment, it's necessary to lowercase DoS (an acronym for denial-of-service) to disambiguate it from DOS (an acronym for disk operating system). I don't think CAOWS has any such problem.

No.

Particularly if it's following a comma because you're not indicating the end of a sentence. If the equation ends in a full point, yes capitalise it.