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Yes; plus the caveat that this draw has to be "truly" random, and have a uniform distribution.

That's not true unless the distribution is uniform. If it were always true, then compression would not work. Compression, in a simple case, often compresses data stored as byte sized chunks into smaller space, precisely because those 8 bit integers do not have 8 bits of entropy each.

Hmm, how many bits has the space of all positive integers?

That's not what the (clumsily written) article is about. It's not about sampling the integers to choose an integer, it's about sampling the prime factors of an integer, as a measure of evenness of distribution of prime factors.

It's measuring the information in the prime factorization, the information in the number as a value.

How does this relate to the mean entropy of 1 noted in the OP article?

Having ripcorded out after realizing the author was trying to prove that water was wet, I'll assume that it's "normalized entropy", in a range of 0-1, indicative of the distribution across the space.