In Rice's theorem, a 'trivial property' is a property that holds for all subprograms (partially computable functions) within a specific language.
If this is what you intended, then the answer to your question is: no, the presence of a trivial property does not mean a specific language is decidable. However, such a property would necessarily be invariant - such as memory safety, purity, or deadlock freedom. Naturally, a program with a non-terminating expansion cannot have any trivial inductive properties that are functions of said expansion.
If you truly mean a trivial property as one possessed by all recursively enumerable languages, then I hypothesize that the only such properties are those directly implied by being recursively enumerable languages, and that also does not imply decidability.