For spousal sponsorship it will not make any difference if you work or not and they do verify the information even everone knows you there but if some how the doubt about something and they find out that you provided false and misleading information they will reject your case for misrepresentation and by law you will be banned from appling for any category for 2 years. So if you take my friendly advice don't take any chances and also I don't see any need either, just provide true information, put the dates of your gap as unemployed/stayed home/looking for job, rest is upto you.
Hope this help.