I'd say it's a little subject to interpretation. It doesn't seem to say that the host is prevented from launching IC for (Level / 2) combat turns, but just that that IC is.
So say the host was spotted you with it's Patrol IC, and you have a level 6 Crack Sprite with you. You command it to use Supression next turn. We'll that turn 1.
The host is planning to track you, so is going to use Tar Baby IC to lock you, then Track IC to find you. It wants to find and arrest hackers, not break their decks.
However, on turn 1 it cannot launch Tar Baby IC, as Supression causes it to be delayed for 3 combat turns. This uses one Sprite task.
On turn 2 it launches Track IC. This cannot do anything to you as you only have one mark from Patrol IC.
On turn 3 it launches Probe IC to mark you so the Track can work.
On turn 4 it can finally launch Tar Baby IC, and also launches Marker IC which to make it easier for Track to get a fix.
Of course, by that time you are probably well out of there, as it hadn't link-locked you !
That's my interpretation, anyway.