First the answer to your question: Yes, it can.
The probably most popular tandem wing was the French "Sky louse" (Pou du Ciel), a design from the 1930's that was built in countless variations.
Mignet HM 14 Pou du Ciel (picture source). The initial type flew with a motorcycle engine of 17 HP. OK, the wings are not of equal size, but nearly. Close enough to count.
But the type had issues due to the small distance between both wings. Please read this answer for details.
And now please do me (and, hopefully, yourself) a favor and see the "lift destroying" elevator with different eyes. This lower lift (or even downforce) is only the consequence of static longitudinal stability, and both can easily be eliminated by shifting the center of gravity back to the neutral point of a configuration. But if you desire to have some natural stability, you will need to accept "lift destruction" regardless of the configuration. To paraphrase a popular song: Birds do it, bees do it …
… even educated flying wings do it, I might continue. Canards, tandem wings, they all will use the rear part of their lifting surfaces less if they want to achieve static stability. And the most efficient way of achieving it is by using the smallest surface of two for this lower lift. This has the additional benefit that the "rear wing" will be entirely within the downwash field of the forward wing, so it will see less angle of attack variation than the wing and be in a uniform flow field.