If we omit "Does" at the end of this sentence:' Does anybody get what I mean" it will become:" Anybody gets what I mean" or "Anybody get what I mean"?
It rather depends what you mean by 'appropriate'; if you mean 'appropriate to a formal context', then you're right - its best not to elide. But in an informal context it's perfectly appropriate to say 'Anybody get what I mean?'. 'Anybody gets what I mean?' is not just 'inappropriate'; it's wrong.
"anybody get what I mean?", becouse you are not asking to one or some person/s in particular
But that sentence is very informal, you can't use in a formal letter or when you're talking to people you don't know. it can be used when you're angry, or talking to people you know well, like your relatives, mates or friends you know since many time ago
p.s. I'm not a teacher so don't trust so much in me