I am not quite sure I understand the situation. Are you saying that the laundry machines would be inside the space that should be reserved for working clearance in front of the panel, and are you asking if the fact that they can be easily moved makes it OK for them to be in front of the panel? If that is the situation, then this would be a clear violation of NEC 110.26. It is not OK for laundry machines, or anything else for that matter, to be in the space in front of a panel, the space being defined as 30 inches wide, 36 inches deep, and 6'6" high.
On the other hand, there is no rule against having laundry machines and electric panels in close proximity, as long as the required working clearance is maintained.