I'll say this because there is no Princeton Law School. I have several friends that went to Princeton for undergrad. I did not. Here's what they told me about their undergraduate experience: Sure, there were a select few truly brilliant, bright kids. Most were not of this kind. Most came from somewhat privileged to extremely privileged backgrounds and once away from home did a MOUNTAIN of drugs throughout their 4, sometimes 5 years. They got through it because, from what I was told, it wasn't that intensive from an academic point of view and there were several more fluffy majors to choose from. It's not all vigorous scholarship, class and decorum in those IVY leagues, you know.
Here's what I think about a poor kid who went to a state or no-name college and pulled a 3.7-4.0.... they're hungry. Add a high LSAT to that and you tell me if the "snob appeal" of your undergraduate institution would still matter.
Yes. (Btw, I graduated from a TTT UG, and my stats are in my profile).
UG does matter, and OP's instinct that, all things equal, a prestigiouos UG grad wins out over someone that attended a crappy school is absolutely credited.