No, use of the indefinite article with a professional title is generally incorrect in standard English. More particularly, it is incorrect when using it as a title:
Incorrect: He is a CIO Smith.
Incorrect: I am an exterminator Jones.
There is one exception: If the speaker intends humourous effect, this construction can be used. It basically says "Yup, that's me, that's what I am. Hahaha." However, it is non-standard.
It is correct to use the indefinite article when the title is used as an occupation:
Correct: I am a CIO, and my name is Smith.
Correct: He's an exterminator. His name is Jones.
Other than occupational or humourous usage, do not use an article:
Correct: He is President Smith.
Correct: I'm meteorologist Eric Burris.
At its simplest, a title works like this:
Is it being used as a title? Don't use an article.
Is it being used to describe an occupation? Use an article.
I heard it as: *Let’s check the forecast out inside WESH dot com. I’m meteorologist Eric Burris*. No article a. However, without your transcription, I'm sure I can't decipher Eric Burris's name correctly. Listening to it once again, there seems to be some syllable between check and the indeed, but check in or checking or checkin' would sound strange. – Damkerng T. – 2013-12-23T06:51:49.647
@DamkerngT. For I'm a poor listener, I've changed OP. And even now I can't present my confident one, neither comment on yours. – Listenever – 2013-12-23T08:01:31.500
2Putting the first few words aside (which I'm still in doubt too, for my listening is also not 100%), I am quite sure that there is no a before meteorologist in this speech. As for English usage in general, I believe that there should not be an indefinite article before job title or occupation before someone's name. I think of it as an adjective before a proper name. And since we don't say I'm a Eric Burris (except for a very rare occasion), I think we don't normally say I'm a meteorologist Eric Burris, too. – Damkerng T. – 2013-12-23T08:16:14.420
1I'm an AmE speaker. He is definitely saying, "I'm meteorologist Eric Burr(is? sh?) – anongoodnurse – 2013-12-23T08:28:00.917
@DamkerngT. I think yours is very persuasive. – Listenever – 2013-12-23T09:37:56.543
1
It's "Thanks for checking the forecast out inside WESH.com, I'm meteorologist Eric Burris" - no article
– Jim – 2013-12-23T21:12:42.230