At least, I don’t think so. This excerpt from Pottermore doesn’t quite mention the Imperius curse, but it comes pretty close:
The Fidelius Charm is not without its weaknesses. If the Secret Keeper wishes to do so, they may divulge the information at any time (although the secret cannot be forced, bewitched or tortured out of a Secret Keeper who does not wish to give up their secret; it must be given voluntarily).
Since Imperius is a form of bewitchment, it seems that you would be unable to obtain the secret directly through Imperius.
There are plenty of creative uses of the Imperius curse that might get you the secret, such as threats or @Shisa’s suggestion in the comments, but I don’t think Imperius can compel somebody to tell you their secret.