If your laptop uses whitelisting (and I don't know if it does or not) then there is no guarantee. If it does have a whitelist it probably does it based on PCI ID, or at least that's how the ThinkPad does it.
What do you mean when it's "not recognized"? What happens? If you put in such a card to do sudo lspci -vvv does it not show up or what? If it does do whitelisting it's probably best to contact HP direct for an "official" card.
