I have been dealing with Chase for a long long time.
Their credit card unit is completely separate from the retail and business banking side. Your opening a checking, savings, loan etc. will not have any impact on your credit card dealings. You may have a personal or private banker coming to bat for you but if the credit card people want A and you want B, you will get A no matter what your Chase private banking people want or ask.
So, basically you can deposit $75K in a checking account, open a $1M investment account and the credit card unit will not care. However, do something fishy with your CC and they will shut it down and maybe even everything else in a blink of the eye.