Room a/c units have part of unit sitting outside window since the is open to rain getting in is it just suppose to evaporate as there is no drain in bottom

Any rain in the pan should not get into the home because the pan is pitched. The heat from the compressor will cause the water to evaporate just like the condensate from the A/C unit

Many window units have a drain. I just installed a GE and it had a small slit drain. The units should be pitched so water will drain over the condenser edge without a separate drain.