Yes, the high voltage (and focus, G2, and many other voltages for other circuitry) are generated from the horizontal sweep in almost every TV set. The horizontal windings of the deflection yoke are an integral part of the horizontal sweep circuitry, and must be present to keep the system working. They could conceivably be replaced with a generic inductor that has the requisite inductance, current handling capacity, insulation rating, and DC resistance.
You would then need to feed your new sweep signal to the existing horizontal yoke winding. You will then discover that the sweep isn't very linear when you move away from a frequency of 15.734 kHz, the frequency that the yoke design has been optimized for. You will have a similar problem with the vertical deflection system, which is designed for 59.94 Hz.
In short, converted TV sets make for lousy oscilloscopes. About all they are good for is driving the yoke windings with stereo audio from an amplifier, to produce neat psychedelic patterns as part of a lightshow or whatever. You will never build anything that resembles a useful measurement device.
CRT oscilloscopes use electrostatic deflection plates inside the CRT, rather than electromagnetic coils around the outside of the neck. This is done to achieve useful bandwidth and a to simplify the design of wideband deflection amplifiers which only have to drive a capacitive load at miniscule power levels rather than inductive coils needing tens of watts of drive.
BTW, if you are playing around with this kind of thing, be aware not only of the HV supply to the CRT, but the so-called "low voltage" (130V or so) supply as well. It can supply several amps of current, and is generally not isolated from the AC mains input. It is actually MUCH more dangerous than the 25 kV CRT anode supply, which is inherently current limited.
You also want to be sure to turn the brightness control WAY down when normal raster sweep is disabled. The beam energy in a CRT is enough to destroy the phosphor coating, melt the internal metal shadow mask/grille, and possibly even crack the glass faceplate and implode the tube when it is all focused to a single line or spot in the center of the screen.