My thoughts on washing machine vs sink-and I use both...if the bag is over all dirty and looks like it will need to be scrubbed to get it clean, then I put it in the washing machine. I have put several suede bags in the washer. I think it's easier to get something that's really dirty clean *evenly* in the washing machine. Also, I think it's easier on the leather to roll around in the sudsy water than to be scrubbed. It's hard to evenly scrub the entire surface so you're more likely to end up with a faded spot.
One thing to be aware of if you wet that bag in any way is that I would guess from my experiences with lighter colored bags, it will look worse when it's wet-the brown will show through the color and you'll think you've ruined it. As they dry they look ok though.
I wouldn't be surprised if it faded some but I'm really not familiar with that style. The good news would be that if it's already supposed to be distressed I would guess that bag came with different degrees of distress even when it was new.
I would probably condition it with something like Apple or Leather CPR, but not anything as heavy as Black Rocks. Most of my experience with NuBuck is in shoes so use your best judgement on that.
My thoughts are if it's too dirty to carry as is, and the only way to clean it is to get it wet, overall it's less stressfull to the bag to dunk it. Are the straps removable? If so I'd take them off and either skip washing them or wash them separately.