In American English, yes, one can both pace about and around a room. Both are correct, and both mean the same thing - to walk randomly in the room or possibly along the periphery.
Around doesn't always mean on the outside circumference of something. Two relevant definitions from the OED:
About (adv): 5. In U.S.: = about adv. a. Here and there with no fixed direction; all about, at random; as in ‘to travel around,’ ‘to fool around’.
About (prep): 4. U.S. (a) Hither and thither over, at random through, about; as in ‘to travel around the country’. (b) Of time, amount, etc.: about, sometime near.
In most cases, however, about is not interchangeable with around.
