Forget soundex. Soundex is actually LOSSY on vowels. It would be counter-productive (at least for English). A modified metaphone algorithm would probably serve better.
First off, what language? In Finnish you could probably just turn the strings end-front and do a simple SQL Like. Hungarian too. Perhaps.
English? Not so simple. You need a serious ORTHOGRAPY to FONETICS (Sampa or another representation) /database/. English never had a reform so orto-to-fonetic is illogical. Impossible to "calculate". Retrieve and receive? ie, ei... And loads of other stuff.
Such database might be possible to "scrape" from sources. Oxford dictionary of modern English, perhaps?
You would probably need also the orthographic "lemma" forms, all converted to phonetic representation.
Your biggest road-block would definitely NOT be the RDBMS structure.
I would start by buying my NLP-doctor-friend at the royal university of tech a couple of beers.
Actually, when thinking about this, maybe this is one of the avenues where it is actually prudent to research the use of ML.