For the next 4 years, why not?
Games are 3 15 minute periods. Standard ice rental is for either 75 or 90 minutes at 3-400 dollars per hour. There is a 3-5 minute warmup.
My suggestion would be, once the Zamboni is off the ice, before everyone goes out, Play the National Anthem at that time. There is no law saying it cannot be played without players on the ice.
Just saved money.