Back in the day I knew two people that had the "Barney" converters. They weren't called Barneys by anyone I knew back then, possibly because they were all brown. I never saw a purple one, or heard them called Barney's until I started coming here a lot.
Anyway, both of these people had these converters, and the "diving board" type (prices on converters ranged between "free w/game" to $20 at the time) and both of them couldn't play Mad Stalker on them. It would crash after the opening, I think. I also remember people on the Turbo Mailing List saying that Sapphire wouldn't run past stage 2.
The Kisado was famous for not having this problem, and your converter was made well after the Kisado, so I would think they are probably fine. As Necromancer said though, expect finickiness, as with any cart based system. All these earlier, problematic converters did was exacerbate the inherent finickiness of the PCE card slot anyway. Just a teeny amount of voltage drop messes them up.