If you do well in school, it doesn't matter where you go to undergrad - state college vs university. To what degree do d-schools weight one type of school over the other, only those in adcoms really know and it probably varies from d-school to d-school.
I can tell you from my perspective, I went to a very small 4 yr college where we had only 60 full time students in the science department. I feel I got a better undergrad education preparing me for d-school than a lot of my classmates because we got a lot more 1-on-1 time with the professors because of the smaller student to professor ratio in each class. Plus, we had a couple of courses that those attending big colleges never had available or had too many classes to choose from like embryology (helped in cell biology) and gross anatomy (actual cadaver dissection). In the end, I was able to excel at my 4 yr state college which et me up for my d-school education.