Offgasing of products typically takes 6 months to a year to fully offgas and even then trace amounts can be found. The vinyl itself is a problem from a sustainability perspective because it contains chlorines typically which are harmful to the environment both in manufacturing and disposal.
The adhesive backing may be low odor or not, it depends on the manufacturer. I suggest you request the Material Safety Data Sheet (MSDS) on the adhesive. It will tell you if it contains VOC or formaldehyde and at what level.
I also suggest you consider something besides vinyl such as cork or linoleum tile which they do make as floating click-together floors. Globus Cork and Forbo are two manufacturers to consider. As an architect, I have specified both Globus and Forbo products successfully for such applications.