True Seeing says you can see through illusions, but doesn't say you cannot see illusions, just that you automatically can tell if what you see is an illusion or not. You could say that you automatically succeed your saving throw to disbelieve them, against most illusions anyway.
Lets check what happens when you succeed a saving throw against an illusion:
Saving Throws and Illusions (Disbelief)
Creatures encountering an illusion usually do not receive saving throws to recognize it as illusory until they study it carefully or interact with it in some fashion.
A successful saving throw against an illusion reveals it to be false, but a figment or phantasm remains as a translucent outline.
A failed saving throw indicates that a character fails to notice something is amiss. a character faced with proof that an illusion isn't real needs no saving throw. If any viewer successfully disbelieves an illusion and communicates this fact to others, each such viewer gains a saving throw with a +4 bonus.
Also, Shadow Conjurations are 20% real (made of shadow-stuff) thus even if illusions were invisible to you, that 20% of the summon monster would show up as a translucent monster that is partially real.
A shadow spell creates something that is partially real from extradimensional energy. Such illusions can have real effects. Damage dealt by a shadow illusion is real.