If I'm asked, "兄弟がいますか。" and my only siblings are a younger step brother and younger step sister, should/can I respond "はい、いもうととおとうとがいます。"? Do I need to specify but still answer in the affirmative? Or does my answer need to be negative?
In general, I feel you can safely say yes, especially if you already consider them to be part of your family. Compare 義理のきょうだい (sibling-in-law, i.e. the spouse of your siblings / the siblings of your spouse), which is not usually included in plain きょうだい. I don't think there is any language- or culture-specific occasions where you have to mention the step- part for the children of your parent-in-law.
You might want to share further details depending on the context and to whom you're talking to, apparently, in which case you could use phrases like 血の繋がっていない (i.e. not biologically related), 異父兄弟/異母兄弟 (siblings who share the biological mother/father, respectively), etc.
To avoid step/in laws relation and blood relation confusion, Japanese language do have word as @Yosh mentioned. (ぎりーin laws/related by marriage)
To reveal it or not and to whom you reveal it that is totally your choice. As this is not something related to language, it is your personal decision.
Japanese people greatly respect each other's personal space. If you say 「はい、いもうととおとうとがいます。」 no one is going to ask you ぎりのきょうだいですか？ or けつえんかんけいきょうだいですか？
So, please don't hesitate to either keep it to yourself or say it out loud.