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will the world end?
Nope. I tumble all my bike kit on a low setting and still the sun comes up each day.
Done it a few times - World carried on going, shorts survived. Probably best not do it all the time though.
Assos shorts come with a nice little bag to wash em in, seem to tumble dry ok with them in at a low heat.
I've got a couple of pairs of Assos F1 Mille's and they both go in the tumble dryer (low setting) with all the rest of my kit, I used the bag a few times and then lost interest. I wash and tumble dry my kit after every ride, so the older pair of shorts must have been tumbled at least a hundred times.
Always put them in a wash bag. Stops the lycra getting stretched and thinning so much they become see-through. No one likes riding behind someone with his/her butt crevice smiling at them.