No. A standard activated carbon filter isn't capable of filtering out sulfur. However, these filtration cartridges can remove tastes and odors from water, so you can expect an activated carbon filter to at least remove the hydrogen sulfide smell.
To properly eliminate sulfur, you'll need to use one of the recommended filter systems in this guide. You're better sticking to filter units that combine oxidation with filtration, which will remove the sulfur smell and the contaminant itself.