Will charcoal briquettes (not activated) absorb water out of the air in the house in a subtropical climate?
The body of your question shows that your primary concern isn't charcoal's hygroscopic character per se but it's suitability as a practical means to lower the relative humidity inside your house.

Let's start with it's hygroscopic character: It seems that charcoal indeed displays hygroscopic properties (the propensity to absorb water to itself) to some degree (at least to the extent that it affects it's burning properties).

The subject was treated by this paper, wherefrom the following citation was selected as part of this answer to your question: 


  The charcoal samples placed in the environment with high relative humidity showed an
  increase in humidity by the heightened final carbonisation temperature, with the highest average detected for charcoal produced
  at 750 °C. This was the reason why the charcoal produced in
  this temperature showed higher moisture related to higher porosity
  presenting a larger area available for water condensation inside the
  pores.
  
  The difference between the moisture adsorbed by the charcoal packed in
  two environments can be attributed to more water molecules present in
  the humid atmosphere (RH = 98%) and a greater ease of inducing the
  porous region of the charcoal. This means that the more humid the
  environment, the greater the adsorption of moisture by charcoal.
  
  These two different moisture conditions represent different possible
  situations of charcoal storage where high relative humidity is not
  ideal.


Now if one of the reasons you would like to use charcoal over other means of lowering the humidity inside your house is that you were planning to re-use the charcoal later for it's primary purpose (as a fuel), this means that it wouldn't suit that purpose very well, at least if you don't plan to dry your charcoal as an intermediary step in the process (dehumidify > dry > burn). Water requires a lot of energy to evaporate which would waste fuel if you wanted to use it directly as such after using it for your house.

Now for absorbing humidity, there are other (much better) substances you could use out there: You could for instance use the very safe and well known SiO2 form frequently referred to as "silica-gel", which works very well at higher RH levels, and can be conveniently "recycled" by ~ 1h pass in the oven at ~100-120C. The main weakness of silica gel in your case is that it quickly loses efficiency at higher temperatures that are not uncommon in Florida. If you'd like to be a slightly less conventional, one could recommend Calcium Chloride (CaCl2), a fairly cheap substance which will hold up to ~4 molecules of water for each of it's own up to a temperature of 45°C, and at the very minimum 2 molecules of water for each of it's own at any temperature naturally encountered in Florida.

I hope this helps!