Is an excited atom more likely to emit a photon if there is a similar atom in the ground state nearby ready to absorb it?
The probability of decay to a ground state is independent of the proximity of other atoms, except so far as the wavefunction's change due to the different boundary conditions that the proximity imposes on all atoms in a lattice. The given excited atom will decay with the probability/lifetine for that excited state, in a random direction and there will be a calculable probability of scattering off another atom and exciting the electron. The proximity does not play a role in the lifetime value, and anyway proximity cannot go to values smaller than the potentials and forces that exist within the dimensions of the lattice.
The following interesting phenomenon though is dependent on the existence of many excited states , ( not ground state as in your question) It is not the proximity so much, matter should be at atomic distances, as the frequency of the photon that gives rise to what is called stimulated emission and is the core of laser action.
When an electron absorbs energy either from light (photons) or heat (phonons), it receives that incident quantum of energy. But transitions are only allowed in between discrete energy levels such as the two shown above. This leads to emission lines and absorption lines.
When an electron is excited from a lower to a higher energy level, it will not stay that way forever. An electron in an excited state may decay to a lower energy state which is not occupied, according to a particular time constant characterizing that transition. When such an electron decays without external influence, emitting a photon, that is called "spontaneous emission". The phase associated with the photon that is emitted is random. A material with many atoms in such an excited state may thus result in radiation which is very spectrally limited (centered around one wavelength of light), but the individual photons would have no common phase relationship and would emanate in random directions. This is the mechanism of fluorescence and thermal emission.
An external electromagnetic field at a frequency associated with a transition can affect the quantum mechanical state of the atom. As the electron in the atom makes a transition between two stationary states (neither of which shows a dipole field), it enters a transition state which does have a dipole field, and which acts like a small electric dipole, and this dipole oscillates at a characteristic frequency. In response to the external electric field at this frequency, the probability of the atom entering this transition state is greatly increased. Thus, the rate of transitions between two stationary states is enhanced beyond that due to spontaneous emission. Such a transition to the higher state is called absorption, and it destroys an incident photon (the photon's energy goes into powering the increased energy of the higher state). A transition from the higher to a lower energy state, however, produces an additional photon; this is the process of stimulated emission.
The materials and boundary conditions for stimulated emission to happen, i.e. increase the probability of emission happens only with special boundary conditions and matter states.
In general atoms in a lattice or in proximity get modified wavefunctions, each affecting the other, but usually the effect is incoherent and usually the electrons are at their ground state. It is only in the special setup of creating a great number of excited levels that the lasing/ stimulated-emission action can be observed.