I don't think that passing crash tests would matter, as insurance companies don't usually make you crash test your vehicle after every modification you make to it.
Seriously though, to make a hardtop car into a convertible you basically just have to hack off the top, reinforce the frame between the A pillar and the B pillar, (if you have a C pillar, then the A pillar and the C pillar) and of course pretty up the sheared off metal where there used to be roof.

Reinforcing the frame is important as most cars will start to "sag" in the middle without the roof holding it together. Though it sounds like it would decrease weight, the frame reinforcement will result in a net increase in weight, even with a rag top. If you want a hard top convertible it's a little more complicated because you need some mechanism to hold the top on.
A targa top is simpler and just as cool, if you ask me. I don't think the frame reinforcement is necesary with a targa top. Either way, the best bet would probrably be to ask around reputable body shops, and see what they say.