The McLeod-Li test can be used as a test of independence and it can also be used to test the hypothesis of no ARCH. In fact, the McLeod-Li test can be used as a general misspecification test against nonlinearity. See Teräsvirta, Tjøstheim and Granger (2010), (pages 140-1 and 178-9).
You may find it useful to know that it is stated in Patterson, and Ashley (2000), (page 40), that the null hypothesis is that the series is i.i.d.
I hope this information helps you, and rather than go into the particulars, I refer you to the aforementioned sources.
As a side note, it's worth mentioning that some tests can be used for a variety of purposes. For example, the BDS test can be used to test the i.i.d hypothesis, but it can also be used to test for the presence of non-linearity. I think this is a similar situation to the usage of the McLeod-Li test.