If you have zero free time, now is likely not a good time to learn your first programming language.
You can do something like the tour at
tour.golang.org, sure. And you can probably have your first functioning program in a matter of minutes. Beyond that though you'll likely be frustrated or confused without some previous underlying knowledge or knowledge of how a machine works. That's not to say you need to know assembly or exactly what goes on in a microprocessor, however.
From my own personal experience, most those I've met that say "oh I need to learn to program so I can build idea x" generally have a one track mind, get frustrated, and don't get very far. If you want to learn just enough to build some idea in your head, you'll likely not have a very good time. I think it takes an interest in programming as a whole rather than a means to create x to really get to a comfortable point. Again, just my experience, I don't want to dissuade you.
In short, if you don't have the time or dedication to put in, you'll likely not be happy with the results. You need some time to reflect, read code, ask questions, play with the language, etc. I do hope you find this time and learn to love programming as I have if it is your interest.
Good Luck,
Alex