Absolutely you can! I did. Went longer with each birth. Dd3's birth was the most pronounced in this regard. I thought I "might" be in labor - a little this and that that made me think so - so called the midwife as we were planning a homebirth and I just wanted to give her a heads up as we live 40 minutes from her and she has kids to transport to her childcare plans.
So it turns out one of our two midwives actually is in our town for another homebirth so will stop by after that to check me. She comes a few hours later, talks to me, tells me I'm not really that far into labor as I am not stopping conversation or doing anything at all noticeable to deal with contractions. But since the midwives are not going to be nearby, and it is my third child, she asks if I want her to check me. I agree to it and the look on her face is priceless. She says "you are an 8..." I hadn't really had any contractions to speak of at that point. Dd3 was the only of my kids to be born posterior though so maybe that plays into it? I would NOT suggest that though - bad, bad idea...
I think MANY women can dilate a bit (1, 2, even 3) without having painful contractions - I think that is fairly common. Much less common would be getting to between a 5 and a 10 without them. But it is definitely possible.
One thing - I wouldn't assume that just because other women in your family gave birth a certain way that you will. I was SO sure that I'd have quick labors because my mom did (really quick, like barely make it to the hospital and left the moment you had an inkling) but dd1's birth was almost 20 hours. I actually think slow and easy is better than quick and hard but to each her own. We don't get to pick anyway.