This question was just asked a few days ago and the answer is it's possible. See the previous thread and comments here: http://ficoforums.myfico.com/t5/Credit-Card-Applications/Maximum-number-you-can-apply-for/m-p/513855...
if the two different lenders don't pull the same bureau, they won't see it. if they do pull the same bureau the second one apped may see it.
Lenders also can do SP pulls whenever they want to after approval, so they could see it in a week or a month.
Shouldn't matter unless your credit is really poor and you're just skating by in approval criteria. Even then it likely won't matter.
It usually takes time for new accounts to show up. Some, like, Barclay, report in about 24 hours, while most report after the first statement.
Inquiries report instantly, and are visible right away to subsequent apps. Assume that any time you try an app spree, issuers can see your previous inquiries.