Do experienced pilots look at the inclinometers during flight?
Yes to some degree but it depends a lot on your seating position.  If your torso is fairly upright and not too well supported, slips and skids become easy to sense, beyond a certain point, as your waist muscles have to work to keep up upright as you "lean into the ball".  

With experience it's possible to stay within, say, half a ball width of centre, without looking at it.  It's tougher if the airplane has reclined seats or has seats with strong side bolsters that hold you in well. 

That being said, you still need to glance at the ball it to keep it really centred while maneuvering and I tend to use both my leaning sense and glances at the skid ball at the same time, leaning sense for large yaw excursions and the skid ball for fine tuning. 

It's a good skill to master when VFR flying because you can keep your head outside the cockpit where it belongs (in VFR) a lot more.

Gliders use a yaw string for skid control and because you are steeply reclining the leaning sense is fairly useless and you rely mostly on the string, which is easy because it's right in front of your face and you don't have to put your head down.

In any case, you still "step on the ball" or "step toward the lean".  It helps to develop the automatic foot action so you squeeze the pedal with your foot instinctively whenever you move the ailerons.  Pilots who learn on gliders have this action fully automated.