Previous examinations of fully convective M-dwarf stars have highlighted enhanced rates of nanoflare activity on these distant stellar sources. However, the specific role the convective boundary, which is believed to be present for spectral types earlier than M2.5V, plays on the observed nanoflare rates is not yet known. Here, we utilize a combination of statistical and Fourier techniques to examine M-dwarf stellar lightcurves that lie on either side of the convective boundary. We find that fully convective M2.5V (and later subtypes) stars have greatly enhanced nanoflare rates compared with their pre-dynamo mode-transition counterparts. Specifically, we derive a flaring power-law index in the region of 3.00 ± 0.20, alongside a decay timescale of 200 ± 100 s for M2.5V and M3V stars, matching those seen in prior observations of similar stellar subtypes. Interestingly, M4V stars exhibit longer decay timescales of 450 ± 50 s, along with an increased power-law index of 3.10 ± 0.18, suggesting an interplay between the rate of nanoflare occurrence and the intrinsic plasma parameters, e.g., the underlying Lundquist number. In contrast, partially convective (i.e., earlier subtypes from M0V to M2V) M-dwarf stars exhibit very weak nanoflare activity, which is not easily identifiable using statistical or Fourier techniques. This suggests that fully convective stellar atmospheres favor small-scale magnetic reconnection, leading to implications for the flare-energy budgets of these stars. Understanding why small-scale reconnection is enhanced in fully convective atmospheres may help solve questions relating to the dynamo behavior of these stellar sources.