Good morning Grigoris -
Yes--if you can find a GQ table to pair up with the total population table, subtracting the two will give you an estimate of household population for that group (e.g. Hispanic/Latino total minus Hispanic/Latino GQ = Hispanic/Latino household population.)
Unfortunately this only works for a limited set of demographic characteristics since not every characteristic is published for group quarters.
If there's a demographic group you're looking for and can't find, there are a couple of options:
Try the Microdata Access Tool https://data.census.gov/mdat/#/ (still in beta version, I think, but worth a try!)
IPUMS https://usa.ipums.org/usa/sda/ (requires registration, but is free and incredibly useful)
Or download PUMS data and extract the variables you want using a statistical programming platform