Can I Register Instrumental Versions of My Songs?

You can register multiple versions of the same song.

Yes. If an instrumental version of a song is being placed in film/TV/advertising (or if you're releasing a remix or a cover), it's a good idea to add it as a new recording (with new ISRC information) under the original song as in the example below:

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One important thing to note is that if you'd like the splits to be different than on the version with lyrics (for example, one writer worked on the music and another writer worked on the lyrics) then you should register the instrumental as a separate song entirely in order to give the writer who worked on the music 100% ownership of the instrumental.