HSN stands for Harmonized System of Nomenclature. It is a system for classifying commodities created by the World Customs organization. U.S. LTL shipping, however, uses NMFC classifications instead.
No. If you claim that your freight is a lower class than it actually is, your carrier will likely find out. They will charge you a fee for reclassifying the freight and charge you the appropriate amount for the actual class of your freight after it has been shipped.
If you don't include an NMFC code on your BOL, it is very likely that your carrier will charge you a reclassification fee and charge you the cost of shipping the freight they they determine your shipment is.