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Multiple comparisons tests, such as Dunnett's, Tukey's HSD, or Bonferroni, may be performed without a significant, "preliminary" one-way ANOVA (many of these tests were created to deal with multiplicity in general rather than be a "next step" to ANOVA). Anyways, if a researcher is using a factorial design that includes two main effects and an interaction (e.g., the associated analysis may be a two-way split-plot ANOVA), then does the interaction (or one or both of the main effects) need to be statistically significant before (s)he can perform multiple comparisons tests or simple main effects tests?

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You should dig further into the results only when there are significant interaction or main effects. If interaction effects exist, the main effects are not that interesting.

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