If I connect the centers to ground instead of a 100k pot, what will be different?
Short answer : no difference to BASIC circuit operation.
Long answer :
It is a 100 ohm pot, not 100K ohm, that I was refering to to reduce hum. To be simpler, then yes, you can forget about the pot and just connect the heater centers to ground. This will work fine with or without a transformer center tap.
Or, you can decide not to connect the heater center taps at all, and instead connect one or the other (but not both) of the other heater connections to ground.
Or you can connect the heater to a dc voltage etc etc etc .....
It makes no difference to the basic operation of the circuit, it just changes the heater to cathode voltage. And you may not need to worry about it, and just ground whichever part of the heater you like.
But, there may be a certain amount of power supply hum coupled into the circuit from the heater to the cathode. And to minimize it you can connect a so called hum pot, the ends of the pot connected across the heaters, and the center tap of the pot to ground. Do not connect any part of the heaters directly to ground. This way you can adjust the pot to the point producing minimum hum.