Are 乒 and 乓 used in classical chinese?
The earliest texts with 乒乓 I can find is vernacular novels of Ming dynasty.

《西遊記》 Journey to the West as an example:

如此二三日，又聽得後宰門乒乓乒乓，磚瓦亂響。——Chapter 10

他掄槍舞劍，一擁前來，照行者劈頭亂砍，乒乒乓乓，砍有七八十下。——Chapter 14

乒乒乓乓，好便似殘年爆竹；潑潑喇喇，卻就如軍中炮聲。——Chapter 16

“乒” and “乓” are used together as onomatopoetic in history. :)