Scott P wrote...
I am aware that you can evaluate two cells for equality using "double equal
signs" -- for example, by entering "=A1=B1" into cell C1 to test cells A1 and
B1 for equality. Is there a way to use this "double equal signs" approach in
place of an IF statement?

It's not double equal signs. The first equal sign indicates that the
cell contents is a formula while the second equal sign is a comparison
operator.

More specifically, is it possible to create a formula such as "=A1=B1
AVERAGE(1,2) "NA""? I have seen a formula such as this that did not include
commas between parameters -- any help on this front will be greatly
appreciated.

Not possible. If you could accept 0 as the result when A1<B1, you
could use

=(A1=B1)*AVERAGE(1,2)

or you could use some other function like CHOOSE, LOOKUP or INDEX
instead of IF, but there's no alternative to using one of these
functions if you want to return different type results (number or text)
depending on whether A1=B1 is TRUE or FALSE.