The integrated sequence has little to do with Common Core. Some districts in Calif have been doing integrated math and integrated science for years. (Personally, feels like another educ fad to me, and it makes it easier to rotate math teachers?)
But the easy answer to your question is to ask the public HS where its top students get accepted. If there are of top OOS privates included, then those colleges obviously see no difference in the curriculum. Of course, you can also demonstrate math proficiency on the SAT and Subject Test 2.
btw: while Purdue and VaTech are fine schools, what’s the rush to pay OOS tuition/fees when you have similar quality schools available in your back yard? (Engineering?)
fwiw: full disclosure, I’m not a fan of paying OOS fees to a public unless you are wealthy or the school is a big upgrade in rankings for the major that you are interested in. For not much more money, you could attend a private college.