Yes. Density does infact affect the rate at which a system can reach thermal equilibrium with another system or so.
When two systems are in contact, there is a heat transfer from the system at higher temperature to a system at lower temperature.
But, transferred heat may be given as,
Therefore, heat transfer depends on the density.
Thus density can determine the amount of heat needed to be transferred among two systems for them to reach thermal equilibrium.
Also the time after which the systems reach equilibria depends on the amount of heat transferred and therefore, density is altogether responsible for rate at which system can reach thermal equilibrium.