This would come up during the obtaining of Conditional Permanent Residency (at the US Consulate or through Adjustment of Status with USCIS), and the main concern is communicable diseases.
The question of the investors health as well as for the spouse and family members, if applicable, will arise at the time of the U.S. consulate interview for the review and issuance of the conditional residency for the investor and family members. Before the U.S. consulate interview the investing family members will be required to undertake a medical examination by a designated doctor approved by the U.S. State Department. The health of the applicant becomes important and if there are signs of the applicant having contagious diseases or being a drug addict or habitual drunkard then there may be grounds of inadmissibility. Therefore it is important to have one's own doctor perform a medical examination first to see if there any issues that may come up in a subsequent medical examination by a designated U.S. State Department doctor.