A simplified monomodal model for stellar and planetary convection is derived for the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of rotation rate as well as with thermal and viscous diffusivities, utilizing a heat-flux maximization principle and a spectrally-local turbulence closure. The convection model is used as a boundary condition for a linearization of the equations of motion in the transition region between convectively unstable and stably-stratified regions, such as the region at the base of the solar convection zone. The equations of motion may be integrated to yield the depth to which convection penetrates into the stable region, establishing a relationship between that depth and the local Rossby number, diffusivity, and pressure scale height of those flows. Upward and downward penetrative convection have a similar scaling with rotation rate and diffusivities, but they depend differently upon the pressure scale height due to the differing energetic processes occurring in convective cores of early-type stars versus convective envelopes of late-type stars. Convectively-driven gravito-inertial waves can be excited at the interface of convective and radiative regions. The magnitude of their energy flux will therefore vary with the properties of the convection. In the context of this convective model, that flux decreases with increasing angular velocity for a given wave frequency, implying that gravito-inertial modes may be increasingly difficult to detect and that they may transport less angular momentum in rapidly rotating stars.