A number of map viewer layers are now available as a Web Map Service (WMS) in ArcMap and QGIS. WMS layers request georeferenced images from a server and display them, but do not download or store the data they are displaying on the computer. This means you can use www.coastalmonitoring.org data directly in a GIS and overlay it with your own data, without having to download individual tiles first. All that is needed is an internet connection and an account on the CCO website (create an account here).
Note that "Image" is the keyword here; the data are viewable (and even query-able with the QGIS and ArcGis identify tools) but it is not possible to change the symbology or use the layers for calculations. For image analysis, raster analysis, creating difference models etc., you would still need to download the data from the map viewer first.