Yes, storing state info in your database will slow things down (whether or not the penalty incurred is acceptable is up to you.)

Maybe I don't understand the problem, but I can't see what difference it makes which server the user uses. Say you send in your text to server A and it sends it back with some suggestions for the misspellings. Then you send the (possibly corrected) text to server B to be written to the database. So what? I don't see a problem with that.

What I would do is have an html form with two submit buttons -- one to spell check and one to commit the text to the database. That way you can spell check to your heart's content and then commit (with possible misspellings) whenever you're ready.