Season 4 of iCarly has just started according to tweets from the stars of iCarly. So it's unlikely that it would start in June. Here are the tweets:
"Awesome 1st day of icarly! I got a feeling, this season's gonna be a good season. This season's gonna be a good, good season. ... Get it? ;)" - Nathan
"JUST received the script for the first iCarly episode of the season!!! I'm so PUMPED right now!!!! I'll start reading momentarily! :D :D :D" - Jennette
"Had a great first day with @danwarp @bruindude92 @jennettemccurdy @jerrytrainor and @munckytown! This season is gonna be the bomb :-p" - Miranda