That is the fuel reg, and you certainly do need it.
At the moment, your engine is running maximum fuel pressure all the time, even at idle and starting. I dare say that the cause of the rough running is due to the engine running very rich and flooding the engine when trying to start.
Reconnect the vacuum line and you will need to get some EFI rated fuel hose to connect the reg to the fuel return line. Id also suggest getting some new spark plugs, those ones are prolly a little fouled from running so rich.