If that is the only way you can get her to eat, yes I think that is or could be a problem. My DD will occasionally watch a show on the weekend while she eats her breakfast or lunch, but the majority of her meals are eaten with us at the table w/ no TV. She doesn't get to watch shows on the phone, etc while we are out at all. My DD is very much a creature of habit though so we often find when we are lax about something 1 time, she wants to always do it. So for example we *never* have the TV on for dinner b/c I don't want to have that battle every night. Same with the iPhone at restaurants- I don't even bring it out as an option b/c I don't want to have to argue with her every time about it.
Our Ped is big on no TV while eating, she gave us a big lecture about it and on the issues that unconscious eating creates- she's a bit uptight about kid/food issues, to be honest.
ETA: WRT the milk, I had this issue with my DD before too. I started giving only water with meals when I realized she was just filling up on milk and not eating her food. At daycare, they get alternating milk/water throughout the day. At home, DD gets one cup of milk when she wakes up (which she often doesn't finish) and then rarely does she get more milk later in the day. I give water with meals and occasionally she will ask for milk with her snack when she wakes up from her nap, which I'll give if she asks. If she doesn't ask for milk, I give water. I never take milk out with us, I always take a cup of water, it's just easier. I never thought my DD would not be a milk-a-holic but she is actually fine with water 99% of the time now and she rarely asks for milk. Or if she does (often when she's tired) and I say I'm going to get her water instead, she is fine with it.