Robie....

Considering the number of rimless rounds chambered in rifles and pistols such as Thomson's Contender series, I'd have to suggest that it's technically safe as long as pressure levels are kept within the limits of the action.

OTOH, with rimless cases there is probably a greater risk of the rim slipping past the extractor. IF this is likely to result in a jam or failure to extract, then it may not make much sense to use such a rifle on dangerous game.

Others will have more exprience than I.

Cheers......... Cooch