Of course. They're meeting the palate of their current country. It even said it was a necessary innovation to keep Americans interested. They're nothing wrong with ordering General Tsao's at your usual local Chinese take-out.
But I should also add in places like Flushing (and I know this from experience), you're going to get better treatment if you don't order General Tsao's or beef and broccoli, etc. They'll serve it to you, but it's American junk food to them. It's like going into a French restaurant and ordering chicken fingers. If you go in at least willing to try the authentic dishes, you're going to get better quality food (and sometimes better prices). It's not a secret why a lot of these places have two menus, only one in English.
But I should also add in places like Flushing (and I know this from experience), you're going to get better treatment if you don't order General Tsao's or beef and broccoli, etc. They'll serve it to you, but it's American junk food to them. It's like going into a French restaurant and ordering chicken fingers. If you go in at least willing to try the authentic dishes, you're going to get better quality food (and sometimes better prices). It's not a secret why a lot of these places have two menus, only one in English.