Absolutely. Experience is a key aspect of dominance, and sexual experience rules the roost. If a woman believes herself to be more sexually experienced than you are, she won't be able to see you as much more than a charming but inexperienced boy at best, and you will perpetually be struggling (and failing) to maintain dominance in the relationship. You can behave as dominantly as you want; she just won't buy into it.
And yes, it's certainly true that some women will wear a calm, "everything's fine" demeanor with you, then go out and engage in craziness when you're not present. It's truly jarring the first time you experience it, when you discover that your perception of reality did not line up at all in some very key ways with actual reality. And women will lose respect for you for not realizing, this is true.
Probably the main indicator of whether a woman's someone likely to go behind your back or not is her accessibility / availability. If she's mysteriously not available some of the time, or she very jealously guards her privacy, or she won't let you accompany her for certain things or with certain social circles if you want to, there's something she'd rather you didn't know. It always sounds like paranoid advice to give ("What, I'm not allowed to have privacy?!"), but the only time I've ever had a woman behave this way was when I was not her only beau. The other big indicator is a precipitous drop in her passion - if you aren't getting her passion, it must be going somewhere else. If she's very sick it's understandable, but barring illness, if this goes on too long, even if she wasn't seeing someone else at first, she'll be a lot more susceptible to (and is probably looking for) someone who can come along and light her fire once more.
If you see one of those, it's a giant billowing red flag. If you see both, waste no time in pushing out the life boats and abandoning ship.