No. It is generally not possible to downgrade the client and certainly not possible to downgrade to previous expansions. However, with some time and knowledge of the inner-workings of the client, you can *sometimes* downgrade one or two versions. It gets harder to downgrade as you go back further since you need to heavily edit the client data and know what is and isn't in whatever version (Removing new items, adding deprecated items, changing DBC structures, etc.). It is possible to do, but not for your average person. If you attempt it, I guarantee you will wind up with corrupt DBCs. It's hard to do major edits to the DBCs without "corrupting" them (Client does a CRC against the server files during initialization, if the client's DBC checksums don't match, no go).
Before Cata, you used to be able to more or less "reset" the client to the base version you installed by deleting the patch MPQs and running the repair tool but with the changes to the way Warcraft updates, it's not possible to do it that way anymore.
Protip for the future: Get yourself a cheap 200GB hard drive and store a copy of every version of Warcraft you have/get. That's what I do. I have v1.12.1, v2.3.4, v3.3.5a, v4.0.6a, v4.2.4, v4.3.4 and v5.4.7 located on various drives. Hell, I even have a copy of v0.7 beta.
