While in theory this is true, in practice, it is negligible in most, not all, but most cases. You are still talking x16 slots and 2.0 cards are fully backward compatible and only a few of the latest graphics cards are able to max out the V1 speeds. I would be more concerned about the motherboard's bus speed, and of course RAM quantities, rather than PCIe versions at this point, and for this discussion.
If you're running a GPU that's PCI Express 2.0 x16 in a motherboard that was only made for PCI Express x16, it'll run, but the connection at the motherboard will constrict the speed of anything going to or from the graphics card.
And regardless, if LordO is unwilling to spend money on more RAM - still the best and most cost effective method - then upgrading the motherboard to get the latest PCIe version is out of the question, as that would likely require new DDR3 RAM and a different CPU, then a new license for Windows too.