Are these SIS Mountain/City Bike Derailleurs compatible with drop-bar shifting?
The rear derailleur shifter needs to be Shimano compatible (and 7 speed) if you want to use indexing (as always, friction always works), while the front derailleur will need to be replaced with a Shimano road FD or you will need to use friction shifters (bar ends most likely) for the front. 

That being said, the bigger problem is the bike fit with these conversions -- the geometry for drop bars is not the same geometry you use for a bike with flat bars for the same person. We've got some good answers on this here (particularly the one by sixtyfooterdude). You'll also need Problem Solvers Travel Agents or special brake levers for the linear pull brakes, so in all likelihood you'll spend significantly more than the bike is worth on doing this upgrade (which might not give you good fit) -- you're better off just buying a road bike (in fact, on such a cheap bike like the Escape 3, you're almost surely better off selling the bike and buying a road bike unless all the parts and labor are free and the result fits you).