Yes, there aren't really any "Jesus Bolts" on a transport category aircraft, and hopefully one of the two pilots would notice gross W&B/CG error. You could end up out of trim, but you should be able to overcome that quickly enough.

And while it's possible to load a regional turboprop aircraft in a manner which might make it marginally controllable, that would actually be hard to do with a pax NB or WB, unless you had a lot of pallets completely full of gold bars.

The one situation that I pay extra careful attention to is heavy aircraft TO on a short runway... it will be fine at max blast but if you get an erroneously large flex/AT number you could end up in the EMAS (or the ditch off the end, whichever). I pay careful attention to the numbers in that situation, and you should feel the accel in the seat of your pants... if not, firewall it or reject. Gentle accel is fine on SFO 28L with 20kts west wind, but not everywhere.

Cargo aircraft are a different story, especially if you're hauling odd cargo like mil tactical vehicles.