My advice would be like Steve Weigand's: give it a try. But start by putting something soft into your backback, like a pillow or some folded towels, and also be conscious of the possibility that clips or zip-pulls on your pack could damage the surface of tatami.
Next, try and get a sense for the direction in which you are rolling. For instance, in practice, mae ukemi is normally from one shoulder to the opposite hip. In that case, all your weight would roll across the backpack. However, you may sometimes have done a rather more "sideways" ukemi where you roll "up one arm, across your shoulders, and down the other arm"; in that case, less of your weight would roll across the backpack. Also, Donovan Waite Shihan has a number of excellent Youtube videos demonstrating ukemi - though he sets a higher standard than I can aspire to.
I once got caught out by the sudden braking of a bus, and momentarily considered mae ukemi down the aisle of the vehicle... but since I was wearing a backback and it had my laptop in it, I just dropped to all fours. It wasn't elegant, but I'm sure ukemi practice meant that I had time to adjust my reaction appropriately.
Hope this helps.