They sure do! Sometimes, circumstances related to relationships you have outside the Government might lead to questions of whether you have an "appearance of a lack of impartiality." (Link to 5 CFR 2635.502 for more information). In other words, ask yourself whether a reasonable person who is familiar with the facts would question your impartiality.
Example: An SGE working for the General Services Administration has made an offer to purchase a restaurant owned by a local developer. The developer has submitted an offer in response to a GSA solicitation for lease of office space. The SGE would be correct in concluding that a reasonable person would likely question her/his impartiality if she/he were to participate in evaluating that developer's or its competitor's lease proposal.
If you or your agency ethics officials determine that your impartiality is likely to be questioned, your ethics officials must decide whether you may participate in a particular matter. Your agency may determine that the interest of the Government in your participation outweighs the concern that a reasonable person may question the integrity of the agency's programs and operations.