Well, to avoid being too technical, this is what I will comment:
If you place your dry cabinet near the air con, your dry cabinet is going to work harder to keep the contents dry. This is because when the dry cabinet is near the air con, it is going to be colder than normal. Below is a rough relationship between temperature and humidity. I will consider a normal day in Singapore at 32 deg and 50% in the cabinet.
Temperature Humidity
32deg 50%
31deg 53%
30deg 56%
29deg 60%
28deg 63%
27deg 67%
26deg 71%
25deg 75%
24deg 79%
23deg 83%
So assuming if you set your air con to 23 deg, between the day and night, the dry cabinet will have to work harder to remove the extra humidity from the cabinet. But when the monring comes, the cabinet is dry and the air con is turned off, the humidity may drop to almost 20%! Further, since you place the dry cabinet near the aircon, the temperature may be as low as 18 degrees! So if your dry cabinet does not dry the cabinet fast enough, you may find that there may be occasional condensation inside the cabinet.