It's okay for a low probing voltage, but with 13.8V I doubt it would survive long, even if your 13.8V supply's current limiter is set to a value around the nominal current that would flow through the transformer if it was connected to 230V. The thing is that for DC the transformer is just a short-circuit; only with AC the current will be limited by the circuitry on the secondary side of the transformer.

_{(* Yes I know that's redundant)}