Yes a dentist can pull a tooth that is broken off even if the tooth is broken off at the gum line.
Although if the tooth is broken off at the gum line or is below the surface, or impacted the tooth extraction will require a more involved procedure.
That means it won't be a simple tooth extraction and will usually require more x rays of the tooth and gums to see what needs to be done to get the tooth extracted when it's broken off.
I have had a tooth that was broken off at the gum line and the dentist was able to extract the broken tooth but it took a bit more work than just extracting a tooth that is not broken off.
It can take a week or more before the dentist will pull the broken off tooth due to x rays and more examinations but it can be done.