'I couldn't find anything detailing the weather conditions at the time, but assumed it was VFR below the cloud deck.'
They started out at ~35,000' and were scudding through the tops of the cumulonimbus from the inter-tropical convergence zone near the equator. To get the icing on the pitot tube they would have had to be in cloud at least part of the time, I believe they were in clear air when they pitched up, but then would have been in cloud most of the way down. The artificial horizon should have been working the whole time though as it gets its information from a gyroscope.
Your second paragraph is true, I know they've looked at it for military UAV operators but I'm not sure about airline pilots. I'm sure I've read something about it being tried in a simulator though.