Not sure how the quad processor would feel about other channels
being left out of something to do; in so much as one quad, in place
of a dual-core, leaves a lot of missing connections and functions.
You may simply choose to upgrade the firmware so a later OS X
may be able to run; that may be a better bet. And more RAM if
the unit still has less than full upgrade capacity. Also, there are a
few good SSD upgrade units that may allow it to run a lot quicker.
Other upgrades may include graphic cards; however the MacPro1.1
is old enough to wonder if one compatible is still available now. If
not new, there may be something else. And graphics may also see
a firmware update; although I'm not certain about that. The GPU is
an area of performance that could be improved; an upgraded card.
Back to a swap of one CPU upgrade to Quad-core CPU + other one
left a dual-core CPU. ~ I think a CPU swap would be non-compatible.
More than a few technical reasons why come to mind.
Good luck & happy trails! 🙂