Ethernet only runs at set speeds, it's not like DSL with training.
As such, if it can link at 1Gb/s, it will do 1Gb/s if the devices are capable of pushing that much.
Also, Cat6 isn't rated for a particular speed. It's rated for a particular standard over a particular distance. It's basically specified to run 10GbE at up to 55m, or GbE for 100m plus a 5m stranded patch cable at each end.