Unfortunately, no. All the case status will say is that a notice was issued on xxx date, but it won't disclose the contents of the notice. If the site shows that correspondence has been issued, however, you may try to call their 1-800# and attempt to get the date that way.
However, be aware that the information on the website is not always updated right away, so I wouldn't trust it. Perhaps a better alternative would be to have someone in your house who can check your mail and be on the lookout for correspondence from USCIS.
[This answer is for general purposes only; it does not constitute advice and does not establish an attorney-client relationship.]