I've personally conducted hundreds of USCG boardings and supervised over a thousand.
The founding fathers, namely Alexander Hamilton, established the Revenue Cutter Service in 1790 to combat smuggling. 14USC89 (read it) charges the service, now the USCG, with enforcing all federal laws in federal waters and aboard US-flag vessels on the high seas. If you want the protection of the US flag, you're subject to inspection. 14USC89 has survived numerous legal challenges. If you're in a foreign territorial sea, the USCG may ask permission from that country to enforce US law aboard your boat in their waters and, although it may take a few hours, they will most likely get permission. Same goes for foreign flag vessels at sea - the USCG may ask permission from that flag state to enforce internationally recognized laws aboard their vessel, and they will most likely get permission.
All USCG boarding officers are also US Customs officers ("all US laws") and as long as you're in customs waters (inside 12nm) you're subject to customs search as well. No probable cause is required - you choose to operate a boat in the US, you're subject to inspection for compliance with all federal laws.
A CG Auxiliary inspection is a good idea and Auxiliarists have the time to do a bit of training, but the sticker is no guarantee that you won't be boarded. When a Coastie asks the date of your last boarding, he or she may ask for the paperwork. A recent boarding is no guarantee that you won't be boarded.
The search and seizure concepts that apply to your house and home don't apply to a boat. You can't take your house to Columbia and there's nothing in the Constitution about choosing to live aboard a boat. Underway or at anchor, it's the same law. If a boat is moored to a pier, the USCG consider it part of the beach and will defer to shoreside law enforcement, but they may assist with a dockside boarding. Dockside boardings after a search and rescue case are the exception.
The vast majority of USCG boardings are "preventive search and rescue" - they want to inspect your vessel and its equipment during the day so they won't have to rescue you offshore in the wee hours of the morning. All USCG stations are training stations.
If you appear to have been drinking heavily, the CG will use one of several tests to determine your sobriety. If you're over the limit according to the state waters you're operating in, they will escort you to the pier where the locals will take over. Only the operator must stay within the limits - your guests and crew can be falling down drunk if you allow them to.
Be courteous and recognize that these dedicated USCG men and women are doing a challenging, dangerous job. Be somewhat sober and have the proper documentation and equipment and everything will go just fine. These young Petty Officers display tremendous restraint when dealing with people that think they know the law and resent the intrusion. We had little 14USC89 cards for these folks to read while we conducted the boarding. Remember that the same Coastie that boards your boat in the morning may deliver a dewatering pump and expert help in the middle of the night.