No... and I've seen a lot of engineering drawings.
Paragraph 3.3.16 Square Symbol ASME specification, the text does says " ... that a single dimension applies to a square shape shall...".
Let's focus on "square shape". Depending on how one defines square shape drives whether the symbology can be used to indicate a square pattern of features as well as a square feature of size.
Fig. 3-11 illustrates a square feature of size however there are no other references.
It would be my inflection that the square symbol could be used as a specification for a square hole pattern however, since it is a grey application I don't recommend it.
Sometimes the great debate in the heat of getting an engineering drawing out the door isn't worth it. Keep it typical and simple.