The short answer is yes, carbon can adsorb mercury from water but is more commonly used for vapor-phase mercury removal. I can't find literature on whether it captures methyl mercury (the bioavailable form). See section 8.
Regrettably the question as posed here is unanswerable. FWIW the most common concern with methyl mercury is exposure via the food chain, not directly from drinking water contaminated by it. It bioconcentrates in fish.
Nobody in customer service will be able to provide guidance because they cannot possibly know. What kind of carbon is in the filter, how much is there, what's the flow rate and contact time, what's the contaminant concentration in water, what's the water chemistry, how fresh is the carbon...the variables pile up into a gigantic heap.
The array of carbon types is vast, in itself.
I've worked with groundwater and soil contamination cleanup using GAC, but typically for solvent and fuels contamination. The interesting bit is when it removes radionuclides and the carbon vessels become "hot" and the carbon itself becomes radioactive waste.