The question in this thread isn't the motor setup, it's how much power an Integra's automatic transmission can handle.
So can we please stop debating over the merits of motor building strategies and STAY ON TOPIC? :a:
To address the OP's question, there are aftermarket solutions to address the weak points within the OEM auto transmissions.
Search for "built automatic" in this forum and you'll get the names of two companies that I found that will rebuild and upgrade the transmission internals to handle the power of a turbo'd B18C1.
*** UPDATE: Here's the link. It took less than 5 seconds to find, which speaks volumes about the power of our search engine.
https://www.honda-acura.net/forums/s...c+transmission
Personally, I wouldn't turbocharge your setup until you have the money and downtime available to upgrade the auto transmission first.