Will it harm 12VDC LED light strips if I supply them with 12VAC instead?
Depending on the type of LED element and the driver circuit, you could either be fine or significantly shortening the lifespan of your lights. If the instructions or markings don't indicate that AC is acceptable then it's probably not. 

However, a failure is not likely to be dangerous or cause a fire. 

So you have to decide if the hassle of replacing burned out LED lighting later outweighs the hassle of giving it the proper power now.