No, the higher the count goes the closer it becomes to the single removed ball not mattering at all, so the only thing that matters is the information you got about which urn you're selecting from.

According to the original poster on Twitter:

"One cool thing is that this probability doesn’t change if you replace 100 in the statement of the problem with some other number (as long as it’s at least 2), as these arguments show."

Source: https://x.com/littmath/status/1752167731682492522?s=46