Sometimes they investigate and sometimes they don't. But you will be questioned about the legitimacy of your marriage regardless of whether there is a formal investigation or not.
There is a possibility that USCIS/ICE will investigate. However, there is no guarantee that they will or will not investigate and/or question you about your prior marriage.
There is a very real possibility that it may be an issue. You should be prepared to deal with the "issue" if you think that it may be a problem for you. The key is to be properly coached for the interview. You will want to speak to a qualified immigration law professional in advance of the interview to prepare properly.
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