Yes, the Peach is considered to be almost on the same plane as the Outback. It's not a traditional New Year's Day Bowl, but it's a much better bowl than the Music City/Liberty/Indy/Papa John's level bowls. In reality, the Indy and Papa John's bowls fall another tier below the Music City/Liberty.
Regardless, I still think that if you were to go to those 4 lower tier bowls consistently, your fanbase would eventually start to wonder when something more might come.
Under Sherrill, you went to 3 Peach Bowls and a Cotton Bowl, and you only had 3 losing seasons in his first 10 years as coach, so he did have some decent bowl trips mixed in periodically, not just a bunch of lower tier bowls. You're right that I don't know how MSU's fanbase would react if you had a string of lower tier bowls, but then again, you've never had a string of lower tier bowl appearances.
This was our string:
1997: Motor City
1998: Independence
1999: Independence
2000: Music City
2001: stayed home at 7-4
2002: Independence
2003: Cotton
That was 6 years in a row where we finished the regular season with either 6 or 7 wins. Once you've experienced those kind of seasons enough, you start to wonder when you're going to make the next step. I'm pretty sure that if Croom were to put together six straight seasons of 6 or 7 regular season wins, you'd have fans getting restless as well. For that matter, you already have fans talking about Croom's process in building your team to a championship level. If you reach a certain point in that process and stagnate for long enough, your fans will get restless.