Bad Company 2 was a very taxing game in its day, especially because of the map size and the destructibility. Laptop video cards are much underpowered compared to a desktop pc.
Regardless, video cards don't cause long load time. I believe that's the job of the cpu and ram. BC2 is a very cpu intensive game and again, laptops are very underpowered compared to a desktop.
I will say that the higher end nvidia cards tend to outperform AMD's, but honestly, and this is my opinion, anything higher than a 660ti or 7950 and it's pretty much overkill at 1080p. I say that because with those cards you can still play BF4 at that resolution at much over 60fps average and with high qulity.
Then there's the whole thing between DICE and AMD and their Mantle ****. That's a whole separate issue.
No, the long loading time was known to be linked to the AMD cards in this case. The devs even posted that on the support forums. It was 65 seconds to load into a multiplayer game. But you are correct, long loading times usually are the fault of the CPU, RAM, and hard drive.