HP's are instantaneous. As soon as you have an HP from an app, it will be visible on a subsequent pull on the same bureau. "Hiding" HPs or new accounts doesn't really work now, regardless, as almost all lenders will monitor your reports w/ SPs after approval and will shut down a card if they see credit-seeking activity that spooks them.
As to your specific case, I'd generally recommend waiting 6 mo's to a year between apps when building from a young, thin profile. But if you really want both, you could apply for the one that's more important first, and then the other one second. For the one you apply for second, you may get approved or you may get denied, but, if approved, you've got both cards, and, if denied, you were going to try again in 6-12 mo's anyway.
In my case I do this often. Not so much to hide the hard pull because I know that will show up. However, I feel that my score is not affected until the day after the hard pull. I could be wrong but this has worked for me. So I want to get in as many pulls as possible before that score changes.
I also feel I get less of a ding from multiple pulls on the same day, same bureau.
