Russ, trying to keep things simple, my response above was with respect to a passing rainstorm, not internal people load, infiltration due to poor vapor barrier, or negative building air pressure drawing in moisture. And it is with the understanding that this is Alaska, not the Bahamas.
CONDITION 1, PRE-RAIN
Say for example you can have a nice, comfortable day that's 75°F outside and 50% humidity (55°F dewpoint). If the central AHUs are operating normally, they will discharge saturated (~100% RH), 55°F air to condition the space.
CONDITION 2, AFTER RAINFALL
Now, weather gets hot and sticky and starts to rain. Temperature outside increases to 90°F and 100% RH (90°F dewpoint - worst case; will never happen in Alaska). Rain falls. If the central AHUs are operating normally, they will discharge saturated (~100% RH), 55°F air to condition the space.
Notice any difference between the two discharge conditions? The only difference is that the chilled water control valve (or compression stages for the refrigerant) will be open wider or operate more, and more water will come out the condensate drain during hot and humid conditions.
Establish design criteria from ASHRAE (I believe Alaska design conditions are included). Cool the air centrally to allow the system to cool and dehumidify based on design conditions. As Quark says, ensure you have a good vapor barrier. And ensure your building is slightly positive (more air in than out).
I don't see an advantage of desiccant dehumidification over the standard method of cooling the air centrally, in this case. -CB