Our traveler appears in a medieval world that with knowledge of the modern world. Maybe he has a copy of wikipedia in his head. He decides to take over the world but he does not take the normal path of gunpowder. Instead he invents long range communications with some sort of wireless telegraph. Could he do this in the 1500s or so.
Oh, yes, easily.
Creating wire by various different methods has been around for at least 4000 years (for jewelery and decorative purposes).
A sheet of metal was cut into a strip and drawn through progressivley smaller holes in beads to smooth and elongate it. (A a big sheet and a helical strip could produce great lengths without the need for joining). Soft and conductive metals like gold and silver are particularly suited to this, or in-a-pinch tin would serve.
Two sets of orthogonal hammers were used on bars of metal to form square wire.
Insulation was then simply wrapping in cloth and coating in any of the available natural resins and thermoplatics (wax, rosin, shellac, tar etc.).
The generation of radio frequency waves could then be achieved by creating a disk on a spindal, which would either have fixed magnets (naturally occuring haematite) around the circumference, or slots - the alternating of slots and metal when spun in a steady magnetic field would act as dipoles, with a coil nearby to pick up the alternating field. This would be spun at high speed until the desired frequency was achieved (as in the Alexanderson Alternator). This could be geared (available since circa 400 BC) such that a slave would power it - perhaps working to the rythym of hummed melody to keep the output speed the same.
To modulate the transmission for voice, a magnetic amplifier would then be used (essential in the early days of radio pre-valves).
The aerial would not need to be miles long, just wound around a ceramic in the propper way to form a tuned loaded coil.
The microphone would be a simple carbon-granule affair behind a basic diphragm - like those used in telephones before the 1980s. (charcoal won't do, it does need graphite).
You are now free to conquer the know world and re-draw the maps as you see fit.
Short answer: no, I don't believe so.
Science and technology are two different things. Letting aside uniform width conductors for coil wires, magnetic materials for coil cores, etc, you do need at least vacuum tubes.
Which do require technological advancement in glass making (to match the dillation of glass and electrodes) and refractory metals for the electrodes (tungsten) and precision mechanical works.
Sometimes I think Edison's bulb was revolutionary not because it brought the electric light, but because it showed how to build a fillament that doesn't burn when it gets to high temperatures.