The consensus on Talkbass (from the threads I have read) is that 1/2 step down tuning works well on the Drop. For my uses with Spector 5 strings and 18 volt active circuits, I can hear latency with the signal. With headphones and using the Drop, I can hear myself hitting the strings and the resulting sound is hitting my ears with a noticeable delay. Normally, the sound I hear from hitting the strings is instantly transmitted to my headphones. In the end, I don't use the Drop. Maybe you will have better results; it's worth a try.
How many different tunings are you talking about? If the open strings are not being used too much, it will probably be easier to stay in one tuning and let your fretting hand do the work. However, if the guitarist is using a lot of open strings and chugging out lots of low notes, you might need to tune to what he is doing.
