Is it considered a faux pas to tweet a prospective agent to ask a question? In my case, an agent I follow has my first three chapters, but I've revised based on agent feedback. I sent a tweet to ask if she would like the revised chapters, or if she likes to make up her own mind about what needs revising. I've had no response. Now I'm wondering if I crossed a line. But if I didn't, and she is that dismissive, I'm wondering if this is an agent I want to work with.
That odd snapping sound you hear is my jaw closing in on your derriere.
DO NOT EVER DO THIS.
And by "This" I mean conduct business conversations on Twitter.
Don't ask about your personal queries on Twitter. Don't ask if she's read the manuscript. Don't ask if she's taking queries. Don't ask if she's behind on her reading.
Twitter is a PUBLIC forum. You have no control over how your tweets are perceived. I cringe every time someone says on Twitter "hey, I sent you an email did you get it" because I think it makes me sound like I'm a slacker about answering my email. While it's true I AM, do you really have to tell everyone?
The other thing to realize is she may never have seen the tweet, or she may not associate your twitter handle with your name or your email. You can't make ANY assumptions about her being "dismissive" based on not replying.
If you've made revisions to your partial or full there is ONE and only one way to ask an agent if she wants the revised version: email her. And use the same email address that you used to query her with. Many of us sort by email address, NOT NAME.
The short answer to your question "Is it considered a faux pas to tweet a prospective agent to ask a question" is YES it is. Don't do it.