I have not tried that, but I am confident to say that KTS is enough on its own. Just store the backups on an external hard drive and disconnect it when you’re done. I believe there is nothing to worry about nor do you have to enable any protection other than Kaspersky.
I don't use Kaspersky, I use F-Secure SAFE, so I can't respond on that combination.
Aside from that, I used it for about a month, it did what it said on the tin well, with no massive affect on resources that I noticed. I went back to Marcium for my backups, if I wasn't a long time user of their products and was searching for an imaging software I'd not turn down Acronis True Image.