It might be useful as a fuse. The voltage is unlimited by the conductor- it will be limited by whatever insulator(s) you are using.
The current will be limited by heating. According to the this Multicore datasheet the conductivity of 60/40 solder is 11.5% of that of copper. It won't be that good compared to a 1mm copper wire because a fair fraction of the solder is usually flux. It's only something like 3% by weight typically, but the density ratio is 8 or 9:1 so perhaps 25% of the cross-section area is flux. So if we assume an equivalent diameter of 0.85mm the resistance should be around 0.26\$\Omega\$/m. If you allow a maximum surface temperature of 90°C that implies a current of less than 2A. The fusing current will be considerably higher, of course.
In normal use the solder layer is a thin layer between copper and copper and the copper also draws heat away, so the solder does not tend to be limiting. And, of course, the diameter of the solder you use does not matter once it's melted in place.