Sorry for the late reply (I forgot to enable tag notifications), from what I can see there is no easy way to do that.
Most of functions that are present in sunpy.io assume the file is local at the very least and while some functions handle URLS, they will error if the file isn’t a FITS file.
What you can do is this however:
from astropy.io import fits
from astropy.utils.data import download_file
url = "https://gong2.nso.edu/HA/hah/201102/20110225/20110225175454Bh.hdr"
fits.Header.fromtextfile(download_file(url))