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Yes, you can, for the same reason you can in other formats.
The first Golden Rule:
They'd have to ban or restrict the card to limit its use, but it's legal in that format.
Sheldon (EDH Rules Committee) has answered this question directly.
Although some rules differ from the official MtG rules (i.e. "outside the game" ,Living Wish, is handled differently than other casual formats), Relentless Rats' ability is covered in CR 112.6m. If Relentless Rats were banned in EDH, you couldn't use any copies, but since it isn't you may use any amount from 0-99 copies because [CR 112.6m] specifically allows you to ignore [CR 903.5b].