Yes, but by definition you can't "cross-chain" with a 1x set up.
Chain's don't know or care which sprockets they're on, but they do care about alignment, and running on less aligned combinations will cause faster wear than on more aligned combinations. So looking at any bike with a multi-gear cassette, wear will be least on the sprocket that best aligns with the chainring, and increase as you move to those on either side of it.
With multiple chainrings the situation is similar, and while folks make a big deal about cross chaining, a quick sketch will show that using the outer with the 2nd innermost involves about the same chain angle as the outer/outer combination.
Cross chain issues aren't digital as in OK/not OK, but progressive, and best, great, good, poor, & terrible.
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