Yes but your other computer on the LAN is connected to the network so it'll see you already spent your coins.
If disconnect both, in order to get a longer blockchain, you'll have to generate blocks; good luck with that.
BTC difficulty is currently 19,339,258.
You'd need to have 51% of the hashing power, hence why it's called the 51% attack.
You kinda left that step out.
You're right - don't turn on the slave system until you've disconnected the internet. The client will sync with your main system. (just add connect=192.168.x.x to the config)
There should be another step in between 8 and 9: Get 51% or more of the hashing power of the coin you want to attack.
Otherwise the valid chain will generate blocks faster than you.
That's usually the hard part since most of us don't have $100k+ to spend
Edit: Sorry for not understanding your post since you left the MOST IMPORTANT STEP OUT.