You question is somewhat dependent on which bank you're applying to. Citi never checks anything of substance, unless you get into trouble (or so I've heard). Chase can be a bit more restrictive. Amex is a different story altogether, as our forums are littered with complaints of folks who have been held up to scrutiny both in the application process as well as those who have Amex cards for decades (without one iota of negative reporting related to their accounts).

Creditboards my be able to yield more in depth analysis on your queries.