If a character has improved targeting does he basically ignore stealth?

Only if it can use Improved Targeting: Hindering Terrain. The other types wouldn't matter.

no he does not ignore stealth, stealth is still active, he ignores hindering terrain.
Stealth would not activate due LoF not crossing hindering terrain.

There is a distinction on what is being ignored. With SP there could be a stealth that activates when LoF crosses water terrain and LoF would not be able to be drawn by someone with IT:Hindering.