Can "in addition to" be used to introduce information not mentioned before in the text?
Yes
Is it weird?
No.
If the context about A is very clear, then it's quite reasonable to introduce new information with A.
For example:
"I was trying to figure out how a person might invest in the real estate market. In addition to buying a few books, I also asked a coworker who knows a lot about it, and checked out a local website with many sales listings."
Fine.
Let's experiment with a different example that has a less extensive intro:
"I recently visited Boston. In addition to buying a few books, I also went to the museum."
This seems acceptable, although maybe a bit hurried.
Finally, if the first part were removed and you started abruptly with "In addition" it wouldn't make sense. You should not introduce a completely new topic with "In addition".