I know little about tandems, but I think the following applies to all bicyclists.
By bicycle you spend about 80-90% of your time climbing on the BRP. This is not exageration. Hills take forever to get up, then you fly down them at 45mph in a few seconds. Repeat 1000X for the full 469mi length of BRP.
Nearly all services avail are a good ways off the BRP. Frequently requiring great descents (then later great climbs).
Camping opportunities directly off BRP are fairly limited and not spaced out well. These tend to be either full RV sites or primitive (wide spot in the trail with maybe a spring nearby), nothing in between.
BRP is driven by 2 types of motorists
1. those using it as a shortcut across town - these folks are speeding, usually in large vehicles.
2. tourists, also speeding (usually), distracted by views, family and passengers, the latest disney dvd soundtrach etc.
Most of the BRP has narrow (or no) shoulders that are often not in good condition.
Despite these factors, many still view the BRP as a nice ride due to the views. There are literally hundreds of scenic views and hiking trails in close proximity to the BRP. It would take you a lifetime to fully take in all these recreational opportunities. The southern end of BRP takes you into Great Smoky Mtns nat park, which is a whole other universe of outdoor rec. Most visitors never leave the car or see even 1% of these areas to which I allude, which makes the whole thing seem a little sad after you've spent time at the BRP.
Timing wise, traffic peaks during "leaf season", which is RIGHT NOW. Probably the worst time to ride unless you ride early/late in day. Views are often obscured by weather too. Nothing more frustrating than saying to a pal "yeh, there in the distance is VA, TN, SC...uh you just can't see past my pointing finger through the the fog/haze".
In winter after the tourists are mostly gone, and it gets cold enough to take some of the haze out of the air, the views open up, you get some sense of solitude. It can be nice then on the BRP. Actually, dead of winter probably the best. Except for the freezing part. And ice on the roadway. Many sections of BRP are closed in winter to motor vehicles, but kept open to bicycle, foot and (occasionally) ski traffic.
Here a "bicycling the brp guide" with keen attention paid to the climbing requirements:
Here's the last tour I read of the BRP. The author apparently camped illegally throughout the trip, although its not obvious from reading journal. If you get caught I think they will arrest you (BRP has its own LE staff, so you can imagine how they pass their time/justify their positions).