More or less, yes. Emphasis is a bit of a vague term though, I prefer to think about it as “what is the thing you’re trying to tell the listener”. For instance if you take the sentence “I did the laundry”, that could be taken (roughly speaking) two ways:
- We’ve already established we’re talking about what I did, and I’m telling you that what I did is the laundry (私は洗濯をした), or
- We’ve already established that someone did the laundry, and I’m telling you that the one who did it was me (私が洗濯をした).
There’s a lot more to the nuance, but explaining all of it takes a whole essay.
Thankfully, someone already wrote said essay so I don’t have to (not that I could, anyway) 
But for now it’s okay to not worry about most of that. You’ll pick up more and more of it as you go along and consume more Japanese material.