No – the value of the posterior density function does not determine the importance of mode. What would matter is the total posterior probability that concentrates around/within the mode.
Unfortunately that typically cannot be accurately estimated using posterior samples unless the Markov chains are able to transition between the modes sufficiently often. When each Markov chain is restricted to one mode there is no information to determine the relative contributions of the two modes.
Note also that the number of Markov chains that converge to each mode also isn’t informative as that depends too much on the initialization (I briefly discuss this in Simple intercept only hierarchical model with two groups: deadly slow, poor convergence - #13 by betanalpha).