Would be interesting to examine how similar runs have affected other schools. Are VCU, Loyola Chicago, George Mason better schools since their runs? Ranking changes in US news? Avg SAT scores of admitted students? Etc
From an Academic Perspective, its hard to imagine the impact would be the same. I know anecdotally the impact on Applications and the such was substantial at a few schools (e.g. FGCU). But St Peter's really is a different type of institution than any of these others.
From a basketball perspective, I think from this century so far the teams that have really made a name form being under the radar in the NCAA Tournament would be George Mason, VCU, Florida Gulf Coast, Loyola, UMBC, and now Saint Peters. The differences between most of the first 5 and St Peters is that those are for the most part much more selective schools. They are also in more desirable areas for potential students from out of the region. Also, I'd assume must casual followers of college sports are/were at least familiar with the CAA schools, Wichita, Loyola while St Peter's is a virtual unknown in many parts of the country. That is part of what makes the St Peters performance compelling.
It really is hard to see this changing St Peter's in a similar way to those other schools. For George Mason, VCU, and Loyola they've been able to upgrade conferences partially off of those runs (Wichita too).
Although it is a different type of school both being public and more selective, UMBC might be the best comparison. While it could be argued what achievement is more difficult, a 16 beating a 1 was always THE thing we were all waiting for. Everybody knew it had never happened while probably many people did not know what the lowest seed to make an Elite Eight was before St Peter's run. For UMBC, I don't think their basketball position has changed so far and I don't think it will change in the near future. Vermont dominates that league and UMBC has been in a group clearly behind them.