"Me, I can't get enough."
Me, I love it.
Sentences like that occur on occasion in spoken/conversational English. However when listening to ESL/EFL students speak, I would take a bit more into consideration. If I kept hearing it all the time, I'd think, "Hey, wait a minute. Something's wrong here."
It may be possible that there is some L1 interference if this sort of sentence were used regularly or too often.
Much would depend on what the speaker really wants to say when considering whether or not there is L1 interference.
Some people like lager. Me, I like dark ale. Me, I like dark ale.
Imagine it with a question mark.
Me? I prefer strong coffee.
It's good for spoken English.
If you are a student of ESL/EFL, my advice is to not find fault in such a sentence if you hear someone whose first language is English use it. It's quite all right in spoken/conversational English.
Moi, je le trouve parfaitement acceptable.
Me, I'm okay with it.
for me, me is lovely with any of its use.
Should have either a question mark at the end of me? or change the sentence to "As for me, I can't get enough".