Technically, it can work. We had an unplugged speaker suddenly start playing radio broadcasts (distorted but recognizable). The speaker cable plugged into it was acting as an antenna and picking up the signals, which the speaker then turned into sound.
Practically, it's unlikely to work and will probably be pretty bad even if it does. Antennas are "tuned" - their length is carefully selected to match the wavelength of the signals it's supposed to pick up. When properly tuned, the passing signal sloshes electrons back and forth along the antenna like you can slosh water in a bathtub. This sloshing works best at a certain frequency (called the resonance frequency). This has the effect of amplifying the desired signal, while reducing the noise from other signals. That's why rooftop antennas have that distinct trapezoidal shape - the different length bars are tuned to resonate a the different desired specific frequencies.
View: https
/i.stack.imgur.com/rzdCm.jpg
If you use a random length of wire (like your house wiring) as an antenna, you most likely will not get this effect. It will pick up a lot more noise than a properly tuned antenna, or worse yet its length may be wrong so that it amplifies the noise while suppressing the desired TV signal. Whether it works or not is completely up to chance (the ratio of the length of the wiring in your home vs the wavelength of the desired signal).
Edit: Also, in the U.S., electrical wiring is required to be run inside metal conduit (to prevent a spark from a rip in the insulation starting a fire). The conduit will act as a Faraday cage, blocking any TV signals.
Just get a proper antenna. The flat "leaf" antennas are really good for their size. And if the signal strength in your area is marginal enough that a leaf antenna won't work, a proper external antenna is much more likely to work that using the wiring in your home. You don't actually have to mount an external antenna on your roof - often they work fine shoved into an attic or top of a closet.