Assuming the existing CPU isn't soldered down to the motherboard, then comes first issue: Does the bios support it? If it doesn't, there is nothing you can do to get it working. And then comes the second issue: The E1 has a TDP of 9W and A6 has 25W, its very possible the existing cooling can't keep the A6 cooled down, so the laptop would have to sit on a really powerful cooling pad forever. Third issue: The existing power supply may not be powerful enough to run it, especially under stress - run any video/game and the system crashes.
Intel I7 3770K @ 4.5ghz, Cooler Master Hyper 212 Evo, Gigabyte Z77X-UD3H, Gigabyte HD7970 ghz edition, 4x4gb Kingston HyperX Beast 2133mhz, Seasonic Platinum 860, Samsung 840 Pro 256gb, OCZ Vertex 4 128gb, WD Black 1TB, WD Green 3TB+1.5TB, ASUS Xonar Essence ST, ASUS VE278Q, Windows 3.11