I’m going to go with: No.
Yeah, it certainly looks like she’s talking on a cell phone. But how the hell would that cellphone work in 1928? I mean, I guess if you unlock the secret to time-travel you can presumably unlock the secret to phones that operate without transmitting towers or satellites, or maybe it’s a future walkie-talkie or something.
But I’m guessing we just assume this woman is talking on a cell phone because we’re now so used to seeing people holding stuff up to their ear and talking that we immediately decode that to mean “cell phone use,” when someone who watched this woman in 1928 might have offered some way more reasonable explanation — like, say, that she’s a crazy person.
Also, it seems to me that if you’re smart enough to travel in time, and then when you get there, shrewd enough to acquire clothes befitting the period, you’re probably smart enough to avoid being caught on camera with some not-yet-invented technology.
Tedquarters 
Very strange indeed. The crazy person theory sounds most plausible. It seems like the area in front of Mann’s Chinese Theatre has always been a magnet for crazy people. Even today it’s packed with people in super hero outfits, mascots, and a midget that pretends to be Chucky and tries to stab people (with a plastic knife, but still). Are we sure that there weren’t walkie talkies or any kind of small transistor radios at the time? Maybe it’s a little jewelry music box? If I time traveled to 1928 though, Hollywood would be a cool place to visit.
I would have to say no as well, but with that being said I can’t really come up with any good explaination other than that a time traveler is really unlikely.
But the video itself is pretty convincing, it sure does look like a guy or woman or whatever it is, talking on a phone.
This person has the technology to travel back in time and get a cell phone to work without any cell towers but doesn’t have the technology for a small concealed bluetooth earpiece or the smarts to not walk around crowded areas with futuristic technology?
It’s entirely possible whatever company put the box set together needed extra footage to justify having a section for behind the scenes footage at the premier. Who knows? I’m sure this gets done. Is it likely they did this and no one in post production noticed the person they filmed talking on a cell phone? Well its certainly more likely than it being a time traveller with a cell phone.
I think the prevailing theory is that it is a Siemen’s hearing aid:
http://hearing.siemens.com/sg/10-about-us/01-our-history/milestones.jsp?year=1924
The explanation is rather obvious. She must be a crew member from the Starship Enterprise who followed Dr. McCoy back in time to Earth in “The City on the Edge of Forever.”
And that was not a cellphone, it was a communicator.
They’re probably testing their hearing aid and adjusting the volume before entering the theatre so they could hear the movie. The microphone section of the style of hearing aids used back then were pretty big.