It really depends what herbal ingredients you're talking about.
Regardless of whether a substance is organic (such as herbs) or whether it's synthetic, if an active ingredient triggers chemical reactions in your brain that cause psychological or chemical dependency, then you can get addicted.
Take marijuana for example. The active THC in it is an addictive substance, even though it is a naturally occurring substance.
Addiction isn't a clear cut thing. Humans can get addicted to pretty much anything that triggers the release of endorphins in the brain (i.e. Anything that gives you a buzz).
Even playing video-games or slot-machines can cause serious addiction problems.
And not all addictive substances are even illegal!