Generally one does not put a comma after etc.:
Books, pens, paper, etc. were strewn all over the room.
However, in your sentence, a comma is needed. This is not because of the etc. but because be it gaming, emails, searching, etc. is in apposition to their daily lives. An appositive is a noun, noun phrase, or series of nouns that are provided as an explanatory equivalent to another noun or noun phrase in the sentence. In this case, be it gaming, emails, etc. provides additional details about their daily lives.
The appositive in this case is non-restrictive, i.e., leaving it off will not alter or make unclear the meaning of the sentence. Consider the following examples:
My sister Joanna lives in Melbourne.
My sister, Joanna, lives in Melbourne.
In both cases, Joanna is an appositive. However, in the first sentence, it is restrictive. The meaning is that I have more than one sister and I'm talking only about this one specific sister; she is the only one of my sisters who lives in Melbourne. Any other sisters I have live elsewhere. In the second sentence, the appositive is non-restrictive, i.e., I'm not restricting the meaning of the sentence to just one of my sisters. I'm saying that I have only one sister, and she lives in Melbourne.
Non-restrictive appositives need to be set off from the rest of the sentence in some way, typically with commas; em-dashes work as well. In your sentence, the appositive is non-restrictive: you're not specifying only parts of their daily life, you're saying people need wireless in their daily life taken as a whole. So you need to put in the comma after etc.
As a further example:
The tools of a writer's trade, i.e., books, pens, paper, etc., were evident on her desk.
Do you see the difference?
That said, your sentence itself is very awkward and sounds unidiomatic:
- Generally, appositives should use parallel punctuation. If you start off with an em-dash, end it with another. Starting with a dash and ending with a comma is inelegant.
- The antecedent of the second it is unclear: wifi? their daily lives? gaming, emails, searching? With the exception of gaming, none of these qualifies as a hobby, and gaming is not an independent subject in the sentence.
- their daily lives—be it gaming, etc. is odd. Perhaps you mean whether for gaming, etc. Gaming, emails, searching is not coextensive with either daily lives or wifi and makes an odd complement to either.
So the sentence is in need of some rewriting.