The short answer to the question "Is it ok to carry your thread on the back of your sashiko piece" has to be another question really. Is the back going to be visible when the project is done?  If it is, then no, don't carry the threads, find a way to either bury them between fabric layers or use the traditional technique of stitching exactly over several existing stitches to start and finish your threads. Also do this whenever you cannot find a continuous stitching line to continue and so have to end a thread.

But if the back is never going to be seen because the project will be lined, then by all means, carry your threads!  

A general rule of thumb for this, if you can't reach the next place to start stitching with less thread than you would use to end the thread and start a new one, then you should end the thread and start again at the new place.

Happy Stitching,

Susan