Colleges make it really hard for out-of-state students to qualify as residents for the purpose of tuition rates. This has nothing to do with being a state resident. I was an out-of-state student while at the U of Illinois but was a state resident as soon as i arrived (well maybe after 30 days don't remember). I had an Illinois DL, paid IL taxes as a resident etc. I eventually filed for a in-state status at the University after 6 years of school and was granted residence by the school, but the entire time I was an Illinois State resident in the eyes of everyone but the University.
Under federal law you are a resident of the state while at school, but convincing the clerk at the gun store without a driver's license may be a another matter.