Does a Root Canal HAVE to Be Done Before Bridge Work/crown?

It only has to be done if the tooth needs it.  Some reasons would be: If the tooth has a large cavity and it is into the nerve or if the tooth has broken and there is not enough tooth structure to place a crown onto it.

Yes, if you have a tooth that needs a root canal treatment it is definitely BETTER to have it done BEFORE any restorations are placed on that tooth.  This doesn't mean that it can't be done afterwards, it is just you will have a much stronger and better looking result and that the root canal doctor would not have to drill through the top of your new crown in order to do the root canal procedure.

When a prosthetic plan is done for a patient the root canal treatment for those teeth is required only if the tooth has a prior problem large deep decay.

Sometimes if the tooth has a bad misalignment it my require a root canal previos to the crown work in order to obtain a insertion path for the bridge but if the tooth has no damage and no misalignment that needs to be taken into consideration it does not need it.

Statistically 30% of teeth hat receive crowns eventually need a root canal but the other 70% would be fine so like I said if non of the previously discussed situations are present you dont need it.