I really hope they don't. I plan to wait for the price to drop before I buy a PS4 so I imagine I'll be using my PS3 for some time yet, like many others. Personally I wouldn't exactly be encouraged to buy a PS4 if the online services for the current gen were switched off so soon. Such a blatant attempt to get at my money would only encourage me to move away from console gaming altogether.
I think 5's servers were shut down in an attempt to get people to pay out for one more PS3 title, yes, but that's not as bad. At least you don't need new hardware to continue playing online. I don't think they'll do the same with 6's servers come the release of GT7. I think they'll stay up for at least a year after it comes out. Such a move would be too obvious a money grab IMO.