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So I took a summer class and the grade came in. Was lucky and got an A+ which raised my gpa. Not a huge difference but any increase looks better. Anyway, I sent out a batch of like 125 mass mail apps on Monday to my primary market.
1) Is it worth it at all to update firms with the grade increase?
2) When would be an appropriate time to do so? Kinda feels like less than a week is a little quick to send an update when they very well probably haven't even looked at my stuff yet.
3) What's the protocol for updating firms, anyhow?

I don't know how to actually go about mass mailing particularly well but I do know that if I received an email from a person seeking a job and then received another email a few days later unsolicited I would think that person is crazy and desperate. Wait until asked.

Odds are it won't make any difference anyways unless it moves your GPA across a natural cutoff like a 3.49 to a 3.5 or move you across a significant ranking marker like top 51% to top 49%.

I would go ahead and send the update unless you are (1) waiting on additional grades, (2) waiting on journal selection, or (3) it was a bullshit course.

While it's true that they might not have looked at your materials yet, you also probably don't have a better time to update them until fall grades come out, and this is hiring season. Not sure why waiting until being asked is helpful--anyone who does contact you (for a screening interview) didn't need to be updated in the first place, and I don't think any recruiting department would ding anyone for updating them in a timely manner. Anecdotally, I submitted a 1L summer associate application missing two 1L fall grades (to meet the firm's application deadline) and updated a week later. Got the job.

If you update, you should simply include a new cover letter concisely and politely explaining that you would like to update your application to reflect recent changes to your resume and transcript, and provide a new set of materials (new resume, new transcript, etc.).

Assuming you aren't waiting to hear about a journal or moot court or something, I would update them early next week. Right now an update might get you to the top of the pile that you will just be at the bottom of again by Monday, so if you wait till end of the day then/start of Tuesday, you might get more mileage out of it.