The wheel being out-of-true will almost definitely solve itself after the two spokes are replaced. Even one missing spoke will result in a wheel extremely out of true.
However, after multiple spoke breakages with no extraordinary cause (like getting gouged by a chain slipping off the top of the cassette), I think all the spokes should be replaced, especially if you are planning a trip or other adventure that a failed wheel could ruin.
The spokes in a wheel work like a chain, and if one link (spoke) has failed due to (presumably) fatigue, all other links have seen the same number of stress cycles and may also fail soon. It is likely the drive side spokes need replacing more urgently than the NDS.
Also, for a heavily loaded wheel like on a tandem, you should make sure the spokes are as close to maximum allowable tension as possible. I believe rim manufacturers give a recommended tension. Under-tensioned spokes are the main reason for fatigue and breakage.
After the first few rides on a newly spoked wheel, the spokes should be checked and re-tensioned if necessary. The drop in spoke tension on a new wheel is enough to put the wheel from 'good' to 'severely undertensioned'. A wheel built by a skilled wheelbuilder will generally not lose as much tension, but it's still good to check.