Depending on the subject, the shot, and the amount of dust, sensor dust can become very visible. While in Arizona a few years ago I got a lot of dust on my sensor because of a side-trip out into the desert and changing lenses without thinking much about it. When I got home I spent a lot of time cloning dust spots out of the skies and backgrounds of many of the shots. Sensor dust normally only shows up in areas of solid color, such as a sky, but they show up there very well.
Virtually every camera that has been used for any time is going to have a few specks of dust on the sensor. I check mine every month or two and blow off the dust that I can. If I leave a few specks I don't worry too much about it until I start to see it in the shots at which time I'll clean it thoroughly. And it isn't a lot of work. It takes, maybe, 10 minutes tops and a couple of sensor swabs.