No, on one syllable words (except a few special circumstances) do not have accents.
Χτες/Εχθές/Εχτές these are the spellings we have in the incubator.
Should the "θ" not be spoken like a "th"? See the example here: http://de.pons.com/übersetzung?q=χθες&l=deel&in=&lf=de (Its a german webpage)
Yes, the θ is pronounced like th. The audio for this word is accurate. From what I hear on the Pons the χ is given too much emphasis. Since this is a one syllable word the χ and the θ sound more like one letter. Try here for Greek spoken by natives: here. Hope that helps.