My gut feel would be "no"....  the cover and fan as designed are to ensure channelled airflow exactly over/through where it needs to be...  leveraging the venturi effect for flow efficiency and pressure.  Without the casing, much of the airflow across the heat exchangers would be lost, making the cards more likely to overheat.  I am happy to be corrected on this...

Personally, my rig has 3 x R9 290's, and after dealing with the noise for the past couple months, I've finally got fed up and have just pulled the trigger on 3 of these:

http://www.watercoolinguk.co.uk/p/Aqua-Computer-kryographics-Hawaii-for-R9-Radeon-290X-edition-acrylic-glass-nickel-plated-version_42990.html

Oh yeah...  and the rest of the watercooling gear to go with them.  Bloody expensive, but will save my sanity and drastically improve the WAF