If you thought of how big Graham's number is, as in learned/remembered every single number in the whole of Graham's number, your brain would quite literally turn into a black hole - not even joking. The amount of information that would need to be stored in your brain would mean that your brain would become so dense it would have the density of a blackhole. Causing your mind to collapse in on itself and form a blackhole.
To be honest, even if your brain had the density of a blackhole due to the information stored in it, you still wouldn't be able to recite the entirety of Graham's number.
And yes, it would form a blackhole and suck the entire earth into it. Why? Because of the amount of matter, there would be no space between matter, unlike the matter within Earth, where most of the space is nothing. If the Earth was squeezed down it would be the size of a pea, so if you though of Graham's number in its entirety not only would you form a blackhole, the information stored in your head would weigh roughly 38, 208 septillion kilograms
So, if you think of the number; all of it, no need to tell. I'll notice when I notice time is becoming heavily distorted