Could the term "holy' (Kadosh ) refer to being 'clean' and being set apart?
The basic answer to your question is "yes", but as always, good questions like this are difficult to answer due to the wide meaning of a Hebrew word like "kadosh" and the typically narrow meaning of the word used as here where kadosh is translated as "holy". But kadosh has much more meaning in Hebrew than "holy" does in English because its meaning in Hebrew is defined by the context in which it is used.
For example, in Leviticus 11:45, in English it reads: "For I am Adonai, ... you are to be holy, because I am holy" (CJB). We have only our understanding of the meaning of "holy" as we know it in our time. But from the Hebrew, it actually carries more of a meaning like this: "For I am YHWH, ... you are to exist as unique ones [or separated people], given that I am unique [or separated]."
The Hebrew word kadosh is probably most often used to mean "separate" or "unique", but carries with it the quality of "special", "sacred", or "elevated", and that is the part that earns the translation as "holy" in English.
So Leviticus 11:45 is revealing that just as YHWH is separated from this world and unique, He is not withdrawn from the world He created, similarly, we become kadosh not by separating ourselves from the world, rather, we are to strive to be separated or be sacred from or elevated from the world through our proper living by YHWH's Word.
So you are correct that part of the meaning of kadosh is to be set apart, as being "clean" is part; but clean is more related to being set apart than it is directly to being kadosh. That's likely not a good explanation, so let's look at Leviticus 10:10.
In English, Leviticus 10:10 reads "so that you will distinguish between the holy and the common, and between the unclean and the clean" (CJB). Notice that holy and clean are correctly listed as two distinct things, yet clean is actually part of the concept of holy. Here it is from the Hebrew with the Hebrew meanings provided:
"[so you will] make a separation between the special and the ordinary and between the dirty and the clean".
Here, kadosh means separated and special, while dirty (or unclean) comes from the Hebrew "tamei" which means defiled or fouled, and clean is from the Hebrew "tahor" which means "pure" in either a physical, ceremonial, or moral sense.
So while being "clean" is part of being kadosh because clean is separated from dirty, clearly something that is clean is not necessarily kadosh or Leviticus 10:10 would not have needed to list them separately.
We hope this has helped because it is hard to describe as most of us do not have a Biblical Hebrew upbringing to understand the scriptures from a Hebrew context.