Racing: Drop Handle Drop Length
To add to Andy's comment, there are so many factors at play that you won't know if a deeper drop gives you any aero gain at all without something like a wind tunnel. 

Changing the position may or may not give you a second or two over 100k, but you also have to consider your power output may or may not be less in the "new" position, which could negate any aero gains. If say that's worth considering, to get to your question. 

Moreover, I think comfort is a bigger consideration. If you're not comfortable in the new deep drop position your power output will almost certainly be less over any significant distance. 

Try it before the race over a shorter distance on a route you ride regularly and compare. Or, get on the rollers with your new bars and have someone watch/record you. Is your back straight? If so that's good. Are your hips/pelvis rocking more? If so that's bad. 

To summarize, you're not going to know if it's more aero outright but you can weigh and compare the symptoms/boons of a new position and make an informed decision if it will make you faster.