It is highly unlikely that a plantar plate tear will heal on its own without some form of treatment or intervention. The symptoms in the plantar plate from a tear or a “pre-tear” (dysfunction) are due to a mechanical overload. If that overload is still there, then it is probably not going to heal up on its own. However, if you limp and reduce activity levels, then that mechanical overload is reduced so it might heal up on its own, eventually.
The use of plantarflexion strapping to reduce the mechanical overload by preventing the toe from dorsiflexing can certainly give it time to heal. Is that healing on its own? Probably not as the strapping is an intervention. That is how you do get it to heal up; you use strategies like the strapping, like stiff-soled or rocker sole shoes or foot orthotics to off-load that mechanical overload to allow it to heal.
However, those interventions do not always work or work quickly enough, then that is when a surgical repair is indicated.