I have sent quilts to Long arm quilters with double battings. I used a cotton on the bottom and a low loft poly on the upper layer. it came out great. The low loft gave just a bit more definition to the quilting, plus some added warmth.
My Long arm person had not done this prior , but she also loved the effect.
If your LAQ does not want to try this and it is warmth you are going for.. use a wool batting. VERY warm. I have done several wool batting quilts...they are much much warmer than the cotton. They do have a bitmore loft that a cotton and will show of the quilting nicley.