To get the desired behaviour:
using IterTools.partition
isinorder(x; order=<=) = all(t->order(t...), partition(x, 2, 1))
isinorder([1, 1, 2]) == true
isinorder([2, 1, 1]) == false
isinorder([1, 1, 2]; order=<) == false
isinorder ([1, 1, 2]; order=x->true) == true