I imagine it would kill the performance. Right now only the first wall hit per cast ray is used. It can be changed so that a order list of walls hit is used, which shouldn't affect performance too much.
The bottleneck will be the rendering. Right now one sprite is used for each vertical slice. With half walls more than one sprite will be needed per slice. I thought of using only 1 sprite and pasting it many times to a canvas object for the drawing, but I'm not sure if that would improve performance.