Can Flight Simulators (FSX P3D) give you the expecience you need to fly a RW plane?
GdD brings up some good points but that really depends on what you mean by "home simulator" and it depends on the airplane. There are some people that have taken it to the extreme and built simulators that are fairly close to real and provide a solid learning platform not only for the flying but the actual physical operation of the controls. You can fairly easily build a home sim for a small plane that has all the controls and instruments you would see in a real plane and even in emergency situations you will see real warning lights in your sim and be able to mitigate it as you would in a real plane (nothing is stopping you from wiring in a smoke machine either). 

As for the flight dynamics they get more real as time goes on and computers get better and better. I use X-Plane and simulate the Piper Archer I fly in real life which I find to be pretty close to the real thing from a flight dynamics/response stand point. My simulator did a great deal for my cross wind proficiency when I was training. I cant say I learned to fly in the sim but I did a great deal of honing of my skills in my home sim.  


  The sim is a tool not a replacement


If you understand this you will better be able to realize that the sim can provide you a great deal of proficiency and can suffice for training in some (not all) cases. Even the big guys use simulation to train for the real thing (this article provides some nice pros and cons). The FAA even considers approved simulator time to count towards certain things.  

Unless you have a full motion sim at home, the sim wont provide you with the feeling of flying which is very hard to replicate. It wont disorient you in IMC by having G-Forces cause your vestibular sense to distrust the instruments. It wont physically throw you around on a bad cross wind landing with wind sheer causing your knee to bump the yoke. It wont shake you to the point you drop your iPad while briefing an approach plate. It wont spin you until your lunch decides it wants to be elsewhere. These are the kinds of experiences you may only find in a real plane...    

One last thing to consider as well is some what of the reverse case. Aircraft cockpits are actually getting closer to computer based units as time moves on. Its common to see keyboards in airbus cockpits and many of the former steam gauges have been all but replaced with screens. As we move into a more automated era some switches have even been lost to digital control units. Even the flight controls them selves have moved into the modern age with fly-by-wire systems removing physical linkage from the side stick to the control surfaces.