re: Is it possible to replace the video card on an HP Probook 6460b laptop?

Yeah, I think it's really context dependent. I have an i7 that's about 5-6 years old (read: kinda outdated, but it's 4 cores but less than 3 Ghz w/hyper-threading), but 24 GB of RAM and an above-average gfx card and I experienced some issues. Not necessarily with Gamecube games but definitely Wii games (only tried games that could use the classic controller). I know The Last Story would only run at about 70%, though I played through Xenoblade Chronicles with no issues. I raise those specific games not as endorsements but as benchmarks. I looked at the Dolphin Emulator wiki and must of the test builds they would use had similar specs, just with better processors. That's why I think processor plays a significant role. But again, I'm no expert.

ETA: I re-read the thread and if you want to do PC gaming you would probably benefit from some of the other solutions posted here. If it's just for the sake of emulation, I'm not saying you're screwed, I'd just say do your research because nobody wants to spend a couple hundred bucks on something that doesn't really help them out. I wish I had definitive answers for you. Sorry, bro.