I'd advise it . . . one of them blatantly stated that it's purpose was to tailor online ads to my browsing patterns. I'll be interested to see if the Kaspersky permissions "extension" blocks that kind of plug-in in the future.
Anti-Virus programs rarely block AdWare, since it's not technically a "Virus". So Kaspersky probably won't block it.
Usually the AdWare sneaks in when you install some type of software and don't read carefully all the little check-boxes which accompany the software. Usually people race through the installation taking all the default settings, many of which explicitly ask you if you want to install browser extensions designed to do all kinds of annoying things.
These extensions are often associated with programs which are installed onto your system which repeatedly re-add the AdWare extensions if you don't stop them. The best way to stop this (and I highly recommend it), is to go into your Windows Control Panel and run Add-Remove Programs and look through that list to make sure there is no AdWare (or otherwise mysterious) program listed there. Many times you will have to Google the programs you see listed (Google: What is blahblahblah.exe program) to find out what they do. If it says anything about helping you with your shopping ... get rid of it. All those things do is analyze your key-clicks and cookies and then force you onto (or pop up) sales sites.
I hate AdWare. Usually when people complain to me about slow computers and their browser crashing, I find tons of these things clogging up their systems.