Yes, they can be too busy to answer within a few minutes. But there are many other reasons people don't necessarily text back immediately. For instance, I don't keep my phone on my person every hour of every day. It sits in one spot in my house when I'm home and often I don't hear the texts come through. I don't stop every few minutes to see if someone has texted me, either.
It also depends on the person. Some respond relatively quickly, while others do not. I have one friend whose texting patterns drive me crazy. She can initiate a long conversation of back and forth texts, then just all of a sudden quit responding. Or she won't text back for hours or days. Or if I send a series of texts, she will reply to one but not the others.
It's like all other manners: some people have them and some don't.