Dehumidification by desiccants and then using direct evaporative cooling is sort of constructing a perpetual motion machine. As both the processes are isenthalpic(or constant wet bulb), you will be just oscillating on a straight line from your start condition to end condition.

Indirect evaporative cooling is a bit different and you can cool air sensibly(constant humidity ratio). But even this doesn't seem to make sense as I took up one sample calculation.

The conditions are 34C(93.2F) and 78%RH. Generally, direct evaporative coolers can drop air temperature upto 75 to 80% wet bulb depression. For calculation sake I took the same for indirect evaporative cooling also, but this is not the case in practice. If you want to reduce your air temperature to 24C (75.2F) then the WBT of dehumidified air should be 93.2-[(93.2-75.2)/0.75] = 66.5F. RH corresponding to 93.2F DB and 66.5F WB is 24.1%. However, you can't reduce the WBT of the air by desiccant dehumidification. So, though you reduce the humidity ration by going upto 24.1%, the WBT remains constant. At this point, your air DB will go up by about 122F (50C). When you sensibly cool it by indirect evaporation, the RH corresponding to 93F(34C) is 57%, 85F (29.4C) is 72%, 80F (26.6F) is 85%.

Drykor is one company that uses liquid desiccant systems (ofcourse Kathabar is the pioneer) but they use DX system for sensible cooling. LiCl is very corrosive and I have seen almost all installations where ducts were corroded like hell despite the guarantee given by the manufacturers. I myself replaced two such systems with solid desiccant system.

My final suggestion will be to drop this idea for the value of time and money.

Good luck,