Jobst Brandt, the author of The Bicycle Wheel, seems to think there is no advantage. (Great book by the way!) Sheldon Brown's website references Brandt at
http://www.sheldonbrown.com/brandt/tied-soldered.html (see below.) I'm not saying anybody that believes in T&S is wrong, but if you can't believe these two guys...
Subject: Tied and Soldered Wheels
From:Jobst Brandt
Date: December 16, 1996
While writing The Bicycle Wheel, to conclusively determine what effect tying and soldering of spoke crossings in a wheel had, I asked Wheelsmith to lend me an untied pair of standard 36 spoke rear wheels, on Campagnolo low and high flange hubs. I had an inner body of a freewheel machined with flats so that a wheel could be clamped into the vise of a Bridgeport milling machine while the left end of its axle was held in the quill.
With the hub rigidly secured, with its axle vertical, dial gauges were mounted at four equally spaced locations on the machine bed to measure rim deflections as a 35lb weight was sequentially hung on the wheel at these positions. The deflections were recorded for each location and averaged for each wheel before and after tying and soldering spokes.
The wheels were also measured for torsional rigidity in the same fixture, by a wire anchored in the valve hole and wrapped around the rim so that a 35 lb force could be applied tangential to the rim. Dial gauges located at two places 90 degrees apart in the quadrant away from the applied load were used to measure relative rotation between the wheel and hub.
Upon repeating the measurements after tying and soldering the spokes, no perceptible change, other than random measurement noise of a few thousandths of an inch, was detected. The spokes were tied and soldered by Wheelsmith who did this as a regular service. The data was collected by an engineer who did not know what I expected to find. I set up the experiment and delivered the wheels.
In another thread, Jobst says this:
That tying and soldering has no effect was no idle guess. Having inspected many wheels, it had become apparent that spokes at their crossings, repeatedly make and break welds by fretting micro motions, eroding the metal so that the crossing spokes nest into each other in a practically motionless junction. This can be detected by movingspokes at their crossings after substantial use. That being the case, it was apparent that tying and soldering could not affect wheel stiffness because there is no motion to be restrained at this point.
Later, I came across an article from the days of high wheelers, that explained an important feature of Starley's invention of the cross laced wheel. The crossed spokes could be tied with twine to prevent headers (end-overs) when one of the huge spokes broke. Because all racers subsequently had tied spokes, they kept tying them even after high wheelers were replaced by today's chain driven bicycles.