You certainly can, checkout the `get_data()` method available on an `Item` object. You can make the `try_json` argument to False so you always download the JSON data.
The ArcGIS Online Assistant shows you both the item properties as JSON as well as the data resource as JSON. The `get_data()` gives you the latter. To get the item's properties as JSON, cast the Item object as a dictionary like below and write that to a file:
import json
my_item = gis.content.search("","Web Map")[0]
dict_my_item = dict(my_item)
with open ("path_to_webmap_json_file.json", "w") as file_handle:
file_handle.write(json.dumps(dict_my_item))