It's awkward to try to give direct, literal answers to "should I?" and "do I have to?" questions on this site. It's preferable to talk about what the consequences of a certain decision are likely to be.
If you include a second-order, AxBxD interaction term without the first-order BxD term, you are liable to mistake a BxD effect for an AxBxD effect. After all, how would you be able to distinguish the two? (I'm using "effect" loosely to mean a statistical connection rather than a true effect of a cause.)
A first-order interaction necessitates that the connection between one predictor and Y is different depending on the level of a second predictor. Similarly, a second-order interaction necessitates that the first-order interaction pattern and associated coefficient (whether zero or non-zero) is itself different depending on the level of a third predictor. In order to test for this latter difference, one certainly needs to know just what that first-order interaction coefficient is.
Interactions will be to some degree collinear with their component main effects, and higher-order interactions, with their component lower-order interactions. Thus the different terms will compete for shared variance and will "interfere" with the statistical significance of the others. The usual, and my recommended, practice is to include only those interactions that show significant and/or substantial effects, whatever your criteria might be, and to ignore determinations of non-significance for all but the highest-order interactions included in any given iteration of model-building.