There was a recent blog post about how a non-elite MP explorer cardholer was getting additional award availability when signed into their account (albeit mostly economy). I too am non-elite with an explorer card. I've been looking into a trip next year, and have found that in general this is true.

However, here's a weird quirk. Was searching NYC -> BEY departing 3/7/14. There are flights (TK4/TK824 in biz) that only show up when I'm logged OUT of my account! They appear to be bookable, so when I log in, the itinerary holds. Very bizarre. From now on when looking for award seats I'll try both logged in and out of my account!