Not quite, but close.
The 4% rule as initially reported in the Trinity University study didn't quite draw down the original amount over 30 years in the worst historical case. So their conclusion, in effect, was that you could endow a $1K scholarship with $25K and it would always last 30 years, but in the historical worst case not for 31 years. But if you picked a fortuitous starting year, it could last for longer than 30 years; in some cases much longer.
As a practical matter, the small endowed scholarships that I am familiar with would invest the $25K amount more conservatively (maybe 60/40? not sure). They then use whatever earnings happen to be that year as the scholarship amount. So maybe one year the scholarship is $850 and the next year it's $1150.
The rule at the endowment I know about says that if you want to establish your own named scholarship, you have to come up with a minimum - I think it's either $10K or $20K. Amounts below that go into the general scholarship fund. This endowment is for a high school; if you wanted to endow a scholarship at a university the minimums might be higher. The reason for the minimums is that there is overhead in managing the scholarship - they have to keep track of the applicants separately, the scholarship criteria can be different according to your wishes, and they have to do the basic financial accounting to keep track of the scholarship corpus, earnings, distributions, etc. It's impractical for them to do it for what they would consider "small" amounts. But that would depend on the school.
I haven't done it, but my parents did. I believe they made additional contributions over the years to get the corpus larger, and I know that some years when they couldn't pick a single scholarship winner, they would write a check to effectively double the earnings and award the scholarship to two recipients.