Not in Middle English. By 1066, thorn had replaced eth in English writing. Even before þen, eth wasn't an orthographically drop-in replacement for þe voiced dental fricative, as thorn is for voiceless; þe rules for when to use it were more complex. Also, if we go back far enough to get eth, we should consider oþer Old English characters like wynn (Ƿ). In any case, eth was replaced by thorn by þe Middle English period.
It's still used in Icelandic.