I've convinced myself that they can't.
Take for example:
4 4 + 4 /
stack: 4 stack: 4 4 4 + 4 = 8 stack: 8 stack: 8 4 8 / 4 = 2 stack: 2
There are two ways that you could write the above expression with the same operators and operands such that the operands all come first: "4 4 4 + /" and "4 4 4 / +", neither of which evaluate to 2.
"4 4 4 + /" stack: 4 stack: 4 4 stack: 4 4 4 4 + 4 = 8 stack: 4 8 4 / 8 = 0.5 stack: 0.5
"4 4 4 / +" stack: 4 stack: 4 4 stack: 4 4 4 4 / 4 = 1 stack: 4 1 4 + 1 = 5 stack: 5
If you have the ability to swap items on the stack then yes, it's possible, otherwise, no.
Thoughts?
Consider the algebraic expression:
(a + b) * (c + d)
The obvious translation to RPN would be:
a b + c d + *
Even with a swap operation available, I don't think there is a way to collect all the operators on the right:
a b c d +
a b S
where S is the sum of c and d. At this point, you couldn't use a single swap operation to get both a and b in place for a + operation. Instead, you would need a more sophisticated stack operation (such as roll) to get a and b in the right spot. I don't know whether a roll operation would be sufficient for all cases, either.