There are lots of ways to fish a dry fly with tenkara, some even more effective than with a western rod.
1. Dapping. Yes the "D" word. Using a furled line especially, but even with a light fluorocarbon line, sometimes I just use the wind. Skittering a dry with a tenkara rod is nearly irresistible at times and you can get a long way out. Just keep tapping the surface with it.
2. At short distances I can place a dry fly very accurately when there is not much wind, and keep everything but a few inches of tippet off the water. A tippet that will manage the fly is important. For bushy flies I use a stouter tippet than would be necessary with a nymph. You are not going to get as long a dead drift as you will with a western rod, and you need overhead casting room to land it and suspend it, but for those quick takes and a drift of a couple feet especially over an obstruction, a light short line is pretty killer.
3. At longer distances though, the line is going to be used much as a western line would. Yes, I confess it
, I am going to lay line on the water and consequently it must float. This is one of the reasons I prefer a furled line made with floating material. It's why Misako uses a section of Amnesia nylon. It is probably why Yvon uses PVC running line. I love to fish dry flies at times, and you have to have enough weight in the line to cast a bushier dry, and enough floating anchor (now there's an oxymoron) not to drag it away. Though some line is bobbing on the surface, it is usually less than the full length snake I put out there with my 5-weight, and I can still avoid a lot of currents a shorter rod couldn't.
Tenkara is not always a fit, of course. Yesterday as the sun was leaving the hemlock spruce river gorge I was fishing, I was sitting on a boulder 15 feet above a long run that was as black and smooth as a mirror. It wasn't long before a spotted I feeder dimpling the water a mere 18 feet out. The canopy above ruled out any overhead moves at all. The 3 to 4 foot brush at the stream edge completed the window. Even dropping down the bank was going to be tough without setting loose a gravel slide.
I first laid on my moss covered seat and tried to sling shot the dry fly to the water below. The sling shot just didn't have the power to roll out 14 feet of line, 4 feet of tippet, and a bushy Rapidan dry. As I carefully dropped over the edge and creeped my way down the steep bank, keeping a tree trunk between me and my target, several more fish were maddeningly dimpling the surface. Each gravel tick threatened to undo me, but thankfully they stopped rolling before reaching the water. Finally I got my feet planted on the few rocks edging the drop into deep water, and reaching my rod upstream over the brush, got my rod over water, fly in hand.
My wife, who now was just a unseen voice reporting from above the rocky bank, kept up her report, "Oh my there is another one, " and "the same one is coming up again." "Oh Kevin, you've just got to catch one of them."
The only back cast I had was upstream left along the bank, so letting the fly loose, I pitched it, able to keep it off the water, but the forward cast was also parallel...only 12 feet out into the stream. Not close enough for a take. Next, I used the drift to position it downstream, and tried to angle a lob upstream and further out, to let it drift down. I waited on the drift, but it was still too short. In desperation I false cast it back and forth, trying to add a fling to the end of my cast to gain inches into the stream. No go. I had no back cast, and couldn't roll it or sling shot it out there. I added a little nymph for some weight, but was essentially bombing the fish then. They shut down.
I just couldn't get it there with a tenkara rod and a roll cast with a 3-weight would have been a breeze. As I wound my line around the keepers, I swear to you, the fish gave a leaping jump and splash. my wife teased, "I think he's mocking you."
Oh well, sometime you just get story.