An oil cooler is recommended for even a daily driver.. there's no question these cars have oil temperature problems.
If you're concerned about the warranty, have the dealer install it. The Nissan Motorsports is a good cooler, but carries a hefty price tag. Your dealer should also be familiar with purchasing and installing STILLEN products, which covers the same warranty as the Nissan Motorsports version (parts only), but in having a dealer install it, definite good faith. Should shave quite a bit of $$ off the installation.
There have been plenty of consumers and magazine editors that have had trouble with as little as 2 laps on the track, the odds are very good you'll be pushing higher temperatures, and possibly a crappy day with a limp mode situation.
In regards to insurance, it's up to your provider. But I have seen a car totaled at California Speedway with AAA insurance during a driving event, and it was no problem, as it was not a race session (IE no one passing another car), just a high speed instructional event. If you have an issue, that's the route to take, instructional driving training course.