So I looked into this some more: Conditional Text cannot be worked with in InCopy, and I can’t find a way to get Character Styles to link to Conditional Text. In order to not check out the files, I thought I could just make a character style conditional text, and embed the character style nested in a paragraph style, but apparently those two don’t link. Am I missing something, or is there really no way to call a Character Style to use the Conditional Text feature?

I currently use paragraph styles to add drop caps and nested styles, and while nested styles allows you to apply it through 1 letter, drop caps only allows you to apply it through characters or lines. When we have an initial quote, I want (usually) to hide the initial quote from the print version in InDesign and make the first letter a drop cap. I have figured out how to do this for stick-up caps with nested styles, but cannot find the appropriate workaround for using a drop cap, nor can I find a way of styling the drop cap without using that feature in the paragraph style. Below is the instructions I have thus far: do you know of a way to get drop caps through 1 letter instead of through 1 or 2 characters?
1) In all paragraph styles you want to have no initial quote, go to the GREP Styles. In the To Text field, type ^” (which says find quote mark at beginning of paragraph).
2) Make Apply Style hidden_character (or something to that effect), and style that Character Style as 0.1 pt (in Basic Character Formats), Horizontal Scale 10% (in Advanced Character Formats), Color: [None] (in Character Color).
3) Apply any character style you want to “through 1 Letters” in Nested Styles. The Drop Cap option in Paragraph Styles will NOT work, as Drop Caps allow you to apply to Lines and Characters, but not Through 1 Letter. (If you do Characters in Drop Caps, you would need 1 for most paragraphs, and 2 for any paragraphs with the initial quote.)