Yes a toilet that is allowed to continue to run can indeed run your water bill up.
last year I got a high water bill of $200.00 and my normal water bill had only been $50.00 per month.
When I found out the toilet was running due to a bad toilet flapper and then fixed it then my water bill went back to normal.
So yes do get that running toilet fixed so that it won't run your water bill up.
Even a plumber is cheaper than a higher water bill that will result from the toilet running.