No, as the inside of the tardis is actual a different dimension it shouldn't have any effect.
Whenever the TARDIS has been tilted or turned sideways, it has usually been undergoing some form of malfunction that, we can assume, affected any systems to combat inertia within the ship. The TARDIS regularly spins and rocks about without any apparent influence on the interior under normal flight.
In "Time-Flight" (not a story I'd normally recommend), the TARDIS is shown being carried in the hold of a Concorde, lying on its side. In that story, the inside was intially sideways, too, but the Doctor adjusted the internal gravity to let people move around inside, as if the TARDIS were upright. From that, we can infer that the internal "up direction" can compensate for an unusual orientation but it doesn't happen automatically.
- It might happen automatically in some cases, otherwise for passengers caught at the wrong spot when the TARDIS went horizontal, they could be killed in a long fall, or property could be damaged. The fact the Doctor had to use rope and tackle to get out of the crashed TARDIS in Eleventh Hour probably means the damage done to the ship was so great the orientation didn't correct.
@Skippingrock: I really loved that bit because it proved, or at least implied, that the front doors do not have to lead to the control room. Which of course makes perfect sense; as the TARDIS is literally a programmable pocket dimension, the place where that dimension meets the real dimension doesn't have to be one sole area all the time.
So in that episode he likely "moved" the doors to lead to above the swimming pool, which once again shows us some interesting fun with gravity that the TARDIS is capable of having. Really any degree of any orientation sems to be possible with the right tweaks on the controls and wiring.
While Sarah Jane Smith was travelling with the (4th) Doctor, he used an old console room for a prolonged period & the doors led, then, directly into that old console room, rather than into the main one. (I'm sure there were other references in the classic series to the doors being able to open into other rooms, including a cargo area, but I can't currently recall the details.) --22.214.171.124 09:25, September 5, 2012 (UTC)