usually the first is fine as the canal can be cleaned and dressed without the need for xrays, however after that the appointments require xrays the check the length of the canals, have you had the first or are you going for the first?

ETA just re read your post, i wouldnt be continuing with root canal without the use of xray, so if he's going to complete without xrays, id be finding someone else!
if the tooth is settled then id leave the rest of treatment til after the bubs is born