I think it's absolutely mandatory to do whatever the hell works for you. In my case, that would be dreaming up a core idea; a gimmick or hook. Then I craft a story arc for it. Next, I sit down and look for a theme in it, and if it isn't there I start shaping one as a spine for it. Lastly, characters and settings and such. And I bet that would be ruinous for some other Deviants who do it backward or sideways and do it well. Trust your instincts!
Well, first I would say your friend is wrong and his thinking is probably influenced by the way theme is approached in English/literature classes. Theme is one of those things that's going to arise from the story, whether the writer was consciously starting with one or not. The truth is very few themes can be sufficiently reduced to a single statement, and even looking at literature as only being about that statement is to miss the point.
But my guess is that you, and probably most writers, have some particular issue or set of issues that concern you, and some particular thing you are communicating in your work. Every story does this, whether it is on the high or low end of the spectrum. Even if you're not totally conscious of what that is, it's coming through in the work, and that's what leads to a theme. So honestly, I wouldn't worry to much.
As to whether I personally think about themes, yeah kinda. I don't really start out with a particular theme to be communicated, but as I'm working, certain ideas appear and I run with them. Basically, themes tend to develop as I write, while certain concepts might be there from the beginning.
You don't need to write with a theme. I don't go around thinking of themes before I write anything. Very little of what I write has an intentional theme to it. Then again, like a lot of things in writing, its concerning the story.
If I want a theme, then I'm writing for a them. If I don't, then I don't even worry about it. I just write.
I do usually try to have some kind of "theme" in mind, but these tend to develop once I'm already writing. I think it's far more important that your story has some kind of significance, which it will unless you're one of those people who's just writing so they can say that they've written something. It doesn't sound like you are.
When was the last time anybody threw a book down in disgust saying "There are no themes in this!"? A far more common complaint is "This isn't going anywhere."