Nope, 2.0 mono would be also reproduced from the center. In a Dolby Surround system, if L and R are identical, they are routed to the center.
This is broadly correct except that it isn’t quite handled that way by the current generation of Dolby’s upmixer/dematrixer (which is, perversely, simply called “Dolby Surround” even though that was the original name of the really basic home tech they used back even before Pro Logic was a thing). It seems the current DTS upmixer does route 100% to C (unless you’ve got the AVR set to LPF the low end out to your sub or whatever) but Dolby Surround actually sends mid-low sound via a LPF to the L and R speakers, with the majority (but not the whole thing) going to C.
This is presumably based on the hypothetically improved bass response of L and R speakers (which are potentially, though not necessarily, floor standing speakers) vs a C speaker (which is usually 2 woofers and a tweeter in a horizontal arrangement, with somewhat limited bass response and a focus on mids instead). In my setup, which has fairily mid-to-treble focused side speakers, this fails miserably and sounds ridiculous so I force the DTS mode instead for 2.0 dual mono and use “Direct” mode for 1.0 to route to C based on the number of channels alone with no fancy upmixer/dematrixer stuff being brought into it.