To first order, no. The definition of an orbit is that it's a free-fall trajectory — since everything around you is always experiencing the same acceleration as you are, you cannot actually perceive this acceleration without some external reference (like measuring your velocity compared to the Earth, and how fast it changes).
That said, the closer you get to the planet, the steeper the gradient of the gravitational field will be, and so tidal effects will get stronger at low altitudes. Depending on just how eccentric your orbit is, how big your space station is, and how sensitive your measurements are, these effects could be noticeable.
Ps. Since you mention Kerbal Space Program, one way you might be able to observe these higher-order effects would be make a spacecraft built out of two parts that are docked together, rotate it so that the docking port is exactly aligned with the orbital direction, and undock (and kill any relative velocity the undocking might have produced). In a perfectly circular orbit, if you did this just right, the two components should stay at the same distance from each other, sharing the same orbit.
In an elliptical orbit, however, the distance between the parts should expand close to the planet, and shrink when moving away from it. Essentially, this is because, with the parts in the same orbit, their time separation remains constant, but their orbital velocity varies.