Some details missing in your question, but I will try to answer in general.  
A TRIAC operates in an AC circuit, provided that the particular conditions of a thyristor are met, that is, not exceed the **maximum working voltage** and ensure minimal **[holding-current][1]**.

You must not forget that **to synchronize the switching of the TRIAC**, you must take into account the zero crossing of the winding that feeds the circuit of the TRIAC.

If you can ensure this operations conditions, the TRIAC will function in the secondary of an isolation transformer.


  [1]: http://electronics.stackexchange.com/questions/48725/what-is-the-holding-current-on-a-triac