Is it possible to change the graphics card in a laptop and, if so, would a ATI Sapphire 1GB card run modern games on a Acer Aspire with 4GB DDR3 RAM, 500GB Hard Drive and AMD Athlon 2.4Ghz Dual-Core?
From the top, the amount of VRAM attached to a discrete video card is about the least important specification to look at for performance judgment. Next, and your opening question, only the Sager brand's high quality desktop replacement machines offer any kind of ordinary CPU or GPU upgrades (Central Processor, Graphics Processor). All the rest, all brands, are welded into a single monobloc that no longer has any "inside" area to obtain access to.
Desktops remain the correct platform for game playing, although there are some more expensive laptops that are sold as game-capable. At least 95% of all mobile computer devices sold, moreover, do not have game-capable video included, which means the laptop buyer must take his time making sure he gets what he wants, instead of shopping simply on price and appearance.
With regard to discrete video graphics cards, core speed, VRAM speed, shader unit count, and memory system bandwidth are the key specs to compare, when specific benchmarks for programs you want to run aren't available.
Three weeks to one month from now, AMD's new Fusion APUs will start showing up in new mobile computer products, and for the same cost or less, than a system with an Intel CPU and Intel chipset video chip, will have a greatly enhanced graphics capability, with a game-capable version costing less than specifying a discrete card in an Intel based mobile computing system.