Is it the bike in your avatar picture? If so, then the gears won't be affected.
Where on the drops do you hold for a comfortable position? If on the brake hoods, then you will be about 3" forward of the stem, so to emulate this with straight bars, you would need a longer stem or fit bar ends. But the latter will give a very similar position to using the brake hoods so makes the exercise a bit pointless.
If you go ahead, you will need different brake levers designed for straight bars. The road brakes you have now rely on the curvature of the bars to get required leverage.
If keeping the existing stem, measure the diameter of you current bars before you buy. There are some odd measurements out there.
Good luck