Critical stuff shouldn't get a reaction like "gee, he has something in his calendar, well we just skip this 10 mil deal because disturbing him is a no-no and he would be mean to us". Critical stuff is critical, take people out of their meetings, life is about priorities.
But I understand the appeal to control freaks out there, everything is plain and visible (or not, depends how you set it up)
Unless they are your subordinate, so that you are empowered to judge and direct their priorities, it doesn't. Nothing prevents you from sending them a message (or meeting request) acknowledging that you know they have som thing scheduled but you have an urgent need (and explaining the need) and allowing them to make a decision, or Maki g a similar request of their superior if organizationally appropriate. Your urgent need doesn't transform you into their boss.
If I urgently need to meet with someone today and I see they've blocked off the whole afternoon for a 4-hour meeting, it could make a big difference if the 4-hour meeting in question is "Critical presentation to the CEO" or "Weekly HR thing that HR spams everyone with but nobody attends and doesn't matter anyway"