From experience, we haven’t found schools to be judgmental about last minute interviews and tours. They realize that these are students and families with busy lives and who may not live nearby. Also, most schools are happy you found them. In all of our searches we’ve found many schools, even HADES, are welcoming and accommodating at any point. Some have offered post 1/15 visits, especially in this post Covid era.
To the OP, we found it telling if after our child expressed an interest in a sport in our case, if our child wasn’t matched with a member of that varsity team if not the coach themselves for the tour. However, I also know because most schools want your child to feel like more than an athlete or artist that they’ll mix up tour guides. One of our children is at a school that does that but they say it’s often not their best tour because they’re not prepared to answer questions about the school music program. But they also make sure to connect the prospective student with the people involved in they’d interests.