Intuitive answer to subject line without reading post text: Yes.
(If you have to ask...)
Better answer after actually reading the text: Ah, this one is really tough, and increasingly common. Seems like a lot of people are taking a "buffet" approach to dating right now, which they wouldn't describe as polyamory but only because there's no "amory" to it at all. I personally don't like it; I think you and I are in the same boat. So you're not being unreasonable for standing up for what you want.
To me, even though "I'm not entitled" to monogamy (before "the talk"), non-monagamy bothers me. It disrupts the bonding process, at least in my old-fashioned thinking which views sex as a bonding experience and not just something fun and meaningless that people do together. I think that those two views on sex may be fundamentally incompatible, and you may find that in the long term this girl is not going to have the same attitude toward sex that you have. Even if she does stop seeing the other guys and become monogamous with you, you're probably going to feel judged and pressured and at least for a while you'll be wondering about how she's comparing you to others. I personally don't think I can do it. Casual sex has to be just casual, without strings of any kind, and relationship sex has to be meaningful. I can't mix the two. So if I have casual sex with a girl, it's with the understanding that nothing meaningful will ever come of it. If I were in your situation, I would worry that any sexual relationship with this particular girl is going to be casual, and that would really mess with my head.
More monogamous people do exist. There's a bit of a spectrum. A lot of people are basically monogamous only after "declaring a relationship" but there are some who just don't really date around that much. I'm not philosophically opposed to casual sex or sex tossed in with casual dating, but I just don't enjoy the complication, and I'm not so desperate for sex that I'm willing to endure more emotional uncertainty to get it. But that's just me.
You gotta do you. If you don't feel comfortable dating a girl who's sleeping with other guys (and I personally would feel the same way), cut it off and move on to the next candidate who might be on the same page as you. I would not encourage you to wait around for her to become monogamous if only because it probably won't happen and it's a waste of your time and emotional energy.