parenthetical element in noun clause: H., who is my friend, playing

Can parenthetical elements set off by commas be used within noun clauses? For example, is this sentence correct in grammar and punctuation:

1. I would like to see Hayley, who is my best friend, playing basketball.

Yes, provided they don't come in odd places such as just after the.

Your sentence 1 is correct.

Looks fine to me on all counts.

Yes, it looks fine.

The rule is that the commas can be used if the relative clause is non-defining or non-restrictive. Therefore,

The cat that was under the table looked at me. [This cat contrasted to another cat.]
The cat, that was under the table, looked at me. [No other cat in the vicinity.]

Assuming no other Hayleys, your sentence should have commas.