"
Test is alias, so when mail comes, the agents in the alias will get the mail"
Well, this is a problem, right off the bat. There's no ticket number yet. OTRS will just create tickets. If the agents respond to this, they are either going to respond to test@test.com (why? The customer sent an email, and unless test@test.com is a proper mailing list, it's *just* a distribution list/alias/mailing group. Replies will go directly to the customer.)
If the agent is smart enough to remember, the agent should be replying to customer AND otrs. Don't get me started if the agent chooses to reply to customer AND test...
There's still no ticket number.
"OTRS will update agents that ticket arrived."
Why bother? test already told them. Now they've been told twice.
"The agent will respond back via email to customer, [may manually add customer emails,]"
No, the agent responds to OTRS. It's the only way you're going to track this. OR, more properly, the agent uses the OTRS web page to reply to the customer.
"The same response[ as it has ticket id], should be updated in OTRS."
When? If the agent responds to the email that arrives via test, it won't get a ticket id.
" If customer responds again [ as it has ticket id], it should get updated in OTRS and [if has other mail ids, should reach to them also.]"
This would work, (CCs and BCCs will be obeyed, naturally).