No there isn't.
And YES there is to not turning it off.
At the gas company we get AT LEAST one high bill complaint per year tied back to the fact they are running a boiler to heat with, don't turn it off in the summer, and set the A/C low enough that the boiler's t-stat calls for heat. For like a month.
I'm curious if they complain to the power company as well about how expensive it is to run the A/C in a home that has a 100,000 + BTU boiler "giving it all she's got".
I'm personally a big fan of turning off all gas heating equipment in the summer, especially if it has a pilot or FOR SURE in a tank style boiler application where it is going to want to keep the tank hot all summer. It's a hassle to light it all back up in the fall, but think of the money you save on gas.
Phil