I have seen it done this way. But it would be very difficult. That is why most bicyclists use panniers.
If you use a trailer with a bicycle, I recommend planning a road-only route. The only possible exceptions would be where the path is very flat and relatively smooth, like on the Meseta, between Fromista and Sahagun. The remainder of the
Camino Frances is replete with hilly and uneven terrain that will apply a lot of torque to the mounting point for the trailer. Damage to both trailer and bicycle can easily result. There are some sections after Puente la Reina that are also relatively flat, but they are not very long, or constant.
Finally, if you ever share the Camino with walking pilgrims, PLEASE use a loud bell, early and often. They will thank you. IMHO, the "brrring, brrrring," Dutch style stad fiets-type bell is better than a simple one that only goes "ding, ding."
I hope this helps.