Yes, you need the install kit. The install kit simply contains the template for drilling the holes, as well as the mounting bolts. Can you get away without the installation kit? Well, yes... if you want to manually measure the pre-drilled holes in the spoiler and then map those measurements to your rear deck for drilling, and then purchase the bolts/washers from your local hardware store.
My advise is do not purchase the cheaper "OEM-style" spoilers that are available on EBay for under $100 that do not include the installation kit. I've heard horror stories about non-matching paint from these sellers. Definitely spend the extra money to buy a Toyota OEM factory spoiler. I got mine from seller Toyotamall1, which is really Sullivan Toyota in Massachussetts. I got the painted spoiler including installation kit for around $175 plus shipping (about $210 delivered). The paint match was perfect (as expected). See this thread: