Yes they do, and I have been able to shave off $25 here and there from a subsequent booking. While I check and use multiple Asia-based booking sources for a given trip and I don't limit myself to Agoda, they certainly have been reliable and I've been using them regularly for quite a number of years.

Do print out and take the voucher with you--some hotels will want it handed over, others don't care. If you are worried about your booking, you can check with the hotel and they should be able to see your reservation and that it was through Agoda. No different from Expedia or any of the other more famous agents.