Gotta agree, push-ups are great because the simple exercise you do (since you can do it on your floor in front of the TV without making a big fuss) is better than the elaborate training regimen you don't get around to doing.
I would say to directly answer the OP, it probably won't impact your upper body strength "a lot" in an absolute sense, although if you find doing 30 push-ups to be difficult now, then it might make a big difference for you. I'd expect that after a couple weeks, 30 push-ups is going to seem like a warm-up. It's small enough that you're not going to hurt yourself doing it every day. Nothing wrong with that.
I'd also suggest, while you're at it, adding a similar number of crunches to the daily workout. Depending on your fitness level, you should be able to reach a point where you can do push-ups and crunches at that level in 15 minutes or so. For both push-ups and crunches, you should either read around or, better, talk to someone who's experienced just to get the technique right. They're both easy, but like was said above, many people use poor form that can be hard on your back.