Yes, they could. The attack is of medium sophistication and it requires, to go undetected, that they somehow installed a valid Root Certificate as trusted in your computer (and/or browser).
Once done, the request for the index page of the website would be sent via SSL CONNECT, and would go on un-intercepted. You would be connected with the destination website (same as not having a proxy at all, which is why a non-decrypting SSL proxy makes no sense unless you're just masquerading your IP), and the page would arrive signed with the appropriate, authentic certificate. So you would see the correct closed-lock symbol on the browser and so on and so forth.
You would need some utility such as Certificate Patrol for Firefox.
will my Kaspersky notice it and stop it? because i heard kaspersky does some tricky stuff with the https certificates
No, it won't. And the tricky stuff Kaspersky (or ESET, or...) does is exactly the above - it installs an invisible proxy plus a trusted certificate, so that it can decrypt your SSL communications and ensure there's no virus inside.
Otherwise, its Internet protection could never work with HTTPS.