Unfortuantely there are a number of things that can go "wrong".
If the area is too large the download geoprocessing tool should block the request in the UI right away. If the extent is ok there is still a chance for the server to respond with an error due to a node limit by the server. Please take a look at
the geoprocessing messages - they should tell you what is going on and if there is an error (size extent or node limitation, or something else) the error messages will tell you the reason.
With respect to the size of the download extent and the UI blocking it, there won't be an immediate block when running the download model. The model has a different execution logic however the geoprocessing results are always in the logged in the geoprocessing
message and they are accessible through the Results window in the Geoprocessing section.