Ipod touch and Itunes problem...

Hello,
my stepmom deleted itunes off my new laptop that i got for xmas and i just put it back on like two days ago. it said that i was already on another itunes so i had to authorize this computer even though i used itunes on this computer before. i have an ipod touch and i dont have any music on my computer... she didnt just delete itunes she deleted EVERYTHING. so i have 216 songs on my ipod and i want them on my itunes. i backed my songs up (all of them) when i got my touch which was about 4 or 5 months ago. so my question is ...

if i backed up all of my song purchased and not purchased songs will they be deleted if i sync my ipod even though it says "everything will be deleted except what i bought"?