No problem. On the FB950 (and FB500 & FB700, not sure about others), as soon as the trailing edge of the sheet being printed passes the alignment bar, it drops so the next sheet can be set. The printer turns off the vacuum zone in the rear loading area until its ready for the next sheet. When it's ready, it turns the vacuum on, raises the alignment bar and away she goes. There are alignment pins on the load side of the machine so you can put the sheets in the same spot. The 1/32" or so comes from user error putting the sheet in the same spot. This is more of a problem on thinner sheets (think 020 styrene), becuse the alignment pins are chamfered at the bottom and the sheet wants to go under the pin sometimes.
The way we typically run our machine on production runs is to read the first sheet only, use the alignment pins, and then do our best to put the sheets in the same size. On some projects it doesn't matter at all, if they are either full bleed, or parts cut out of the sheet. The small tolerance would only ever become an issue in double sided printing (now your 1/32" is 1/16", which is still usually within tolerance) or on paneled pieces like you mentioned.
If that tolerance is an issue, simply tell the machine to read every sheet. This takes about 30 seconds, which isn't a huge deal if you're running four sheets, but adds up if youre doing hundreds or thousands. f
While your idea of printing many sheets butted up together could work (you'd basiacally just tell the machine you're printing roll stock and butt the boards up manually), I think it would be more problematic than anything. I'd simply print the boards with registration marks and trim accordingly.
Crap, just realized I typed rigid media in the last paragraph above, should say the biggest advantage of a hybrid is being able to run roll media. More capacity for roll stock, and wider widths depending on the machine.