Yes, they do! The church I play at has the worst possible accoustic room for drums, so I'm a master at the quiet drum kit. To be honest, it's not just about getting the drums "quiet". It's bringing lower frequencies out of each instrument to make it appear "quiet".
Sticks:
Hot-rods are a must. I use the smallest kind. I can't remember the name of them, but I have a set of nylon "rods". These work great in my left had on a snare, but not as well on cymbals. If all of that is over kill you can move down from 7A's to even smaller sticks. But be careful, they break easily.
Cymbals:
If it says "Medium", "Heavy" or "Rock" on the cymbal, don't even think about it. "Thin" or "Studio" is a must. And the older the better. Older cymbals have had a chance to cure and warm up. Newer cymbals are a little more harsh. On my kit right now I have a set of vintage 14" Zildjian A hats, an older 14" Sabian HH thin crash, an 16"
Sabian AAXplosion crash, and a vintage 20" Zildjian ride. Thinner cymbals are better for low volume because you don't have to hit them as hard to get a "cymbal" sound out of them. The AAXplosion series from Sabian is great because you barely have to touch them to get a perfect shimmering sound.
Drums:
Small is good. Thin is good. I built a kit specifically for the church I'm at. 10" rack tom, 13" floor tom, and 18" kick. The 18" has a good punch at low volume and sounds like a recorded kick. The toms are both 6ply maple, which is thin for a drum shell. Thinner shells bring out a lower fundamental pitch that make the drums appear quiet. All heads (tom & bottom) on the toms are coated single ply. I have Evans G1, but Remo Ambassadors work just fine. The coating warms the sound, but doesn't kill it like a Pinstripe head does.
Snare:
I use a 5x14" maple snare with wood hoops. I use a Remo Fibreskyn head on the top and a standard snare side head on the bottom. This head is a little thicker which takes away some of the "crack" of the snare. The wood heads warm the sound. Tuning is probably more important on the snare than anything else. I usually tune the snare in the low-medium range to keep some of the high frequencies away.
Hopefully you can pull some information out of that and put it to use on your own kit. I've been collecting different drums, cymbals and sticks for a few years now, so I have some specific pieces that work for me in that situation. I'm currently building a deeper 12" snare to see how that works at my church. Good luck with the quiet drums!