Short answer
You are right, with a few caveats.
Background
Most tinnitus cases are caused by sensorineural hearing loss, as you rightfully indicate, namely due to a loss of hair cells in the cochlea. The deafferentation of the auditory cortex and subsequent chronic inactivity of this region in the brain ultimately leads to the generation of intrinsic brain activity in the auditory cortex, which is perceived as a 'ringing in the ears' (PloS Med, 2005).
Cochlear implantation has been shown in a multitude of studies to ameliorate the symptoms of tinnitus; for a review see Linhares de Freitas Borges et al., (2021). CIs basically mask the tinnitus sounds by swamping it with electrically evoked activity in the auditory system.
A CI is a medical device for treating severe-to-profound hearing loss. It bypasses the damaged hair cells in the cochlea, and restores activity in the auditory nerve by direct electrical stimulation of auditory nerve fibers (Fig. 1). CI is, however, not a first-line treatment for tinnitus and remains in the experimental phase for that purpose, at least as far as I know. Tinnitus has been mainly addressed as a secondary outcome to hearing performance after CI for treating deafness, although prospective randomized controlled trials with tinnitus relief being the primary outcome are underway (Assouly et al., 2021).
However, your idea of a single-electrode 'dummy implant' isn't very feasible, because it is difficult to insert a cochlear implant such that one or more electrodes are in direct electrical contact with the cochlear region corresponding to the frequency (or frequencies) of the tinnitus (Fu & Shannon, 2002). The cochlear regions with hair cell damage differs between patients and depends on the type of hearing loss. Therefore, a regular CI with a multi-electrode array is inserted that covers the better part of the cochlea (barred the low frequencies).
Furthermore, a 'silent' (i.e., below threshold) electrical stimulus would make not much sense, as you wouldn't know when sufficient electrical activity was generated. Rather, these folks are treated with a CI and fitted with a with a clinical program to restore hearing function in that ear.
Another note of importance is the fact that CI results in substantial loss of the residual hearing in the implanted ear due to insertion trauma, and scarring later on. That's why treating an ear with tinnitus due to localized trauma (e.g., noise-induced hearing loss, for instance due to occupation or in professional musicians) may not be a good idea, because a CI doesn't restore acoustic hearing, it allows for the restoration of some hearing function, but it will never be anything like a normal ear. That's why, in general, only ears with severe-to-profound hearing loss should be treated with a CI, including for tinnitus patients (Punte et al., 2011. In the end, it will be a cost-benefit consideration between physician and patient to determine whether the loss of residual hearing weighs up against the chance and extent of treating the tinnitus.

Fig. 1. Cochlear implant system. Source: Mayo Clinic
References
- Assouly et al., BMJ Open (2021); 11: e043288
- Fu Shannon, Ear Hear (2002); 23(4): 339-48
- Linhares de Freitas Borges et al., Brazilian J Otorhinolaryngol (2021); 87(3): 353-65
- PLoS Med (2005); 2(6): e194
- Punte et al., Cochlear Implants Int. (2011); S1: S26-9