I would think if you are using an ultra literal translation, you would have the best chance at doing this fairly accurately, such as Young's Literal Translation. But even then, I think SOOO many words have overlapping meaning, you wouldn't have a clue which of the 15 Greek words to translate the one English word into. So I don't think such a task is do-able IF you are hoping to get a more literal Greek translation out of an English Bible. You certainly will NOT get anything close to the original Greek bible. If you don't mind a more meaning focused Greek translation, I think you could do it.
Adding to the problem of recovering the original Greek manuscript from an English bible, is that most English bibles (including the more literal/form focused NASB) aren't ultra-literal. They go against the "literal" translation philosophy ALL the time. They try to work out some balance between meaning and literalness because too much literalness can cause a loss of meaning. Also they just translate "less accurately" ALL the time with no understandable reason (ALL the critical text English Bibles do this).
I think the best book to read on Bible translation philosophies is "One Bible, Many Versions" by Dave Brunn. In this book, he shows you ENDLESS cases where "so-called literal/form driven" Bibles go against this philosophy in favor of a "meaning focused" translation. All Bible translation is a balancing act between the two philosophies, in my opinion and all translators employ both.