Seth, it is hard to determine if this is EIFS based solely on the pictures however the others are correct in ways to determine the type of stucco present. In the pictures it looks like the material in question in at a covered porch area? If this is the only place it is located with no direct expose to rainfall there is a chance that there may be little or no damage under the siding. If this is EIFS, the installation details are all wrong. Anywhere the EIFS material meets dissimilar materials ie. brick veneer, windows, doors, porch there must be roughly 1/2" joints with sealant in tact to ensure water tightness. The material cannot be in contact with concrete as insulation board will absorb moisture through wicking action and cause damage that way. It also depends on the type of system installed as there are drainable systems that now provide a drainage path for water that penetrates the siding materials. Inspecting this type of siding system should only be done properly trained inspectors. The Exterior Design Institute is a great way to get properly educated to inspect this siding material. I went through the program several years ago have become one of the few inspectors in my area offering this service.