That would be difficult. Deseret script is phonetic, so you'd have to either look up the pronunciation for each word or eat the imperfection from the ~40% of words that can't be easily predicted.

Deseret script as it's supposed to be used is even harder to automate conversion into than that alone would suggest: you're supposed to write the stressed equivalent of unstressed vowels. So the words "photograph" and "photography", for example, should be 𐑁𐐬𐐻𐐬𐑀𐑉𐐰𐑁 and 𐑁𐐬𐐻𐐪𐑀𐑉𐐰𐑁𐐮 (IPA: foʊ̯toʊ̯græf and foʊ̯tɑgræfɪ, my keyboard transliteration: fo;to;graf and fo;tografi). I don't think this is very common in practice, however -- which is a problem for back-converting Deseret to Latin, since the unstressed schwa can be written either 𐐲 or 𐐮 by people who don't distinguish them.

Also, textspeak is built into it: the name of the letter 𐐒 is 'bee', so the word 'bee' can be written '𐐺'. This can even hold within a word: the Wikipedia page has an example of a coin with the text "𐐐𐐄𐐢𐐆𐐤𐐝 𐐓𐐅 𐐜 𐐢𐐃𐐡𐐔". The first word there is 'holiness', but it's written /hoʊ̯lɪns/ (ho;lins), since the name of the letter 𐐝 is pronounced 'ess'. Usually you see this in the definite article, which is just written 𐑄, but you could also write 'entry', 'zebra', and 'jeep' as '𐑌𐐻𐑉𐐮', '𐑆𐐺𐑉𐐲', and '𐐾𐐹'. (ntrɪ zbrə dʒp / ntri zbru jp -- and 'entry' could also be written with a final -𐐨 instead of -𐐮)

It would be possible to automatically convert Latin to Deseret (or Shavian) and back, but it wouldn't be easy, and it probably couldn't be done quickly enough to have a browser plugin do it.

edit: a Latin -> Deseret converter already exists, but it's crap: can't take more than a few words at a time, returns allcaps, adds semicolons for no reason after some letters, can't handle textspeak even for the definite article, and makes vowel choices that I wouldn't make. (Looks like it writes all unstressed vowels with 𐐆.)