We may read Arcadia as a book without ever seeing it on the stage, but the fact that it is a play meant to be looked at on a stage strongly influences how the plot unfolds. While a text on the page must be read in order to make sense, focusing on one moment at a time, putting Arcadia on the stage means that the nineteenth century and the present day can exist within our field of vision at the exact same time. Its status as a play (as opposed to, say a film) also makes the out-of-order historical narrative less jarring. Consider: if we were watching a movie set in the distant past and someone wandered through with a laptop (or wearing a pair of Converse sneakers ... we're looking at you, Sofia Coppola's Marie Antoinette), it might jolt us out of the story. But putting a similar juxtaposition on the stage seems less weird, because we know the performers aren't trying to make the action look real. We're aware, all the time, that a play is fiction.
What's more, while reading Arcadia, we get imagine the play unconstrained by budget or reality, so if you want mentally to cast Will Ferrell as Bernard Nightingale and Robert Pattinson as Septimus, go right ahead.