No, that's definitely an early electromagnetic pickup hanging from the side of the mounting. There would probably be a horseshoe magnet inside that square casing, with copper wire wrapped around it.
Here's a photo of one that sold on Craigslist awhile back, showing the position of the pickup:

- Columbia Kolster.JPG (66.96 KiB) Viewed 884 times
All early electric pickups used thumbscrew type mountings for their needles. While it may be fitted with a removable steel needle, it would probably have originally used a plated needle for multiple plays, or possibly one equipped with a tungsten tip.
Many of the tonearms used for the early electrically amplified phonographs were of the acoustic type. The manufacturers simply ran the wires through them. In that way, the same tonearm could be used for their lines of both acoustic and all-electric models. Looking carefully at the tonearm, though, the opening is far too small to accommodate an acoustic type "sound box" or reproducer.
As far as I know, Columbia introduced it's all-electric line about a year or so after Victor and Brunswick, and all of the Columbia electrically amplified models were of the conventional type fitted with amplifiers and loudspeakers, rather than true horns. In some cases, the early speakers were mounted at the base of small horns for extra oomph, but I don't know if this is true for Columbia-Koslter models. I'd guess that if the seller didn't see the amplifier, it was probably removed at some point.
I should point out that some of the early Victor electrically amplified models DID use the same exponential folded horns that were fitted into their all acoustic Orthophonic models--especially those equipped with radios. The radio was electrically amplified while the phonograph was acoustic. One interesting model, though, is the Victor VE-8-60 which was actually fitted with a tonearm equipped with an acoustic sound box AND an electric (horseshoe magnet) pickup --
http://www.victor-victrola.com/8-60.htm In this case, the owner would pull a small lever which slid an electrically driven diaphragm into the throat of the horn's elbow to activate the electrical playback.
Unlike wind-up type acoustic phonographs, these early all electric models can be an expensive proposition, when it comes to repairs. Of course, ANY early electric phonograph/radio combination will have to have the electrical components overhauled top to bottom before it can be safely used. (The same holds true for the aging record players from about the early 1980s and before. How time flies!)
JDS