Yes you can do this.
I swim pool laps five times per week with my Apple Watch Series 8, previously with a Series 4. The lap counts are accurate. To ensure the accuracy of the heart rate I always tighten my watch band before entering the pool.
On the watch I’ve configured my Pool Swim Workout Metrics to show the following: Time elapsed, Current heart rate, Maximum heart rate, # of laps, Total yards
However without an iPhone you’ll not be able to access all the additional metrics in the Fitness app on the phone.
No need to have your iPhone at the gym. The watch will sync up to the phone when you get home. Good luck!