It's interesting although mobile ISP's like phone providers are moving back to unlimited data, Well it's really limited, and limited because they they sort of throttle you if you use too much. Home ISP's are starting to cap data.
Comcast does it, ATT does it and our local providers do as well. If you're streaming video you're probably OK. They factor in you're going to watch an hour or two of Netflix a day and that shouldn't hurt your data cap, but you aren't able to watch high definition 4K video for hours on end with almost any data service out there. If you send emails and there's photos or music attached that's not going to hurt you either, but sending lots of video or downloading lots of video could be a problem.
What's really going to hurt you is online backup because the question you asked is upload included in your data cap in the answer is absolutely. It's just data that moves between you and the server and online backup can be quite large if you're using Back Blaster or Carbonite two of the best online backup providers. It's a nice idea but it's bad for data caps.
You need to make sure you know what you're backing up and when you're doing it. Some ISP's like Usenet and I wouldn't recommend Usenet for much of anything, but if you're stuck with it they provide free times where you aren't counting against your data cap. Middle of the night for example.
So if you can do your backup then with Usenet you probably won't worry about your data cap. Other providers like Comcast don't have these time controls so you need to worry about it all the time.
Another big problem is an online security camera like a Nest Cam. We have one at my office and it's always sending video up to the cloud. If you're doing that from your home and you have a data cap you could have a problem.
So in answer to your question yes uploads counts and yes they could cause you to hit your data cap long before you think you should.
*Although mobile ISPs moving back to limited unlimited data, home ISP capping data
* Streaming video probably OK, but not 4K for hours on end
* Normal emails even with photos or msuci won't kill your cap, video more of a problem
* Online backup will kill you. Backblaze or Carbonite, nice ideas, bad for data caps
* Make sure you know what you're backing up, and when
* Some ISPs provide free data late at night (Hughes Net) and back up then
* Online security camera, like Nest Cam, a big problem; constrantly uploading video