Sure you'll get a noticeable improvement, but you also have to factor in the cost of a new motherboard also.
Actually, he wouldn't. He's talking about the A8-3870K which is FM1 like his current A6.
As far as whether or not it's worth it, eh, I guess it's an OK upgrade, but I'd go with a more powerful CPU if you're upgrading. Something like a Phenom II X4 or i3 (or even a Pentium G CPU). You will of course need to get a new board for any of THOSE.
Alright... just so I don't have to start a new thread for this question, can I ask it too: would an upgrade to the A10-5800K and FM2 motherboard be a good upgrade? If so... is the IGP in the 5800K much better than the 6530D/6550D?
That would probably be a much better upgrade based just on the CPU power of the A10 alone. And the IGP is a good bit better as well, from what I understand.