You would gain another 'layer' of security. I see security as like an onion. I only bother encrypting emails to ONE person (because they are the only person I email about anything potentially 'odd') and we have a few layers. layers upon layers man. Manual encoding using our own (non sophisticated) cipher method (which key-changes a LOT, but is VERY simplistic and probably easy to crack), then GnuPG and then hushmail it just for that extra layer. The emails themselves are 'sanitized' of any identifying shite, and so on. Also as a rule I only access my hushmail accounts from 'borrowed' WiFi hotspots, wiping router logs when I am done. I tend to also use TOR while doing this.
It is all about the layers man. Each one is another layer of insulation to help CYA
My point is that your are not really gaining anything by using hushmail. As hushmail holds your keys and would gladly sell you out if asked to do so by court order. You would be much better off using your time to secure your own computer in other ways than encrypting already strongly encrypted info with a secondary insecure systems like hushmail. It would be like covering a safe with play-doh and saying "its all about layer man".