Seems super vulnerable to frequency analysis though. However, if this is a path you might want to go down, you might want to look at CryptDB, a research project that looks at keeping a server side encrypted database and allows for queries in a principled way: http://css.csail.mit.edu/cryptdb/

Products like CipherCloud reportedly work like you suggest. Unfortunately it's not very secure.

If you split the text into words, discard case and encrypt each word, the NSA can just e-mail you a dictionary file, match the line numbers in the dictionary file ciphertext to line numbers in the dictionary file plaintext, and they've got your secret decoder ring (at least for every word in the dictionary file).

Something like text search should only need partially-homomorphic encryption. For example: encrypt each byte with the same key. Then to search, encrypt the bytes of your search term and send them to the backend. It should be able to find them without knowing what your search term was. There are issues with this exact scheme of course but you get the idea!