If the pumps do not have internal check valves or there are no check valves in series to block reverse flow, the pressure difference generated by a single pump pumping will cause a reverse flow on the other loop. The amount of that reverse flow depends on the capacity of the pump that's operating, and the pumping head of the in-active zones, and the drag of the inactive pumps. Since that reverse flow is injecting return water from the active zone into that radiation, it'll be warm, but not hot.
In some cases even with check valves there is enough convective force to get some flow, which is a function of the geometry & temp at he manifold.
BTW: An open hearth fireplace runs at about 7% efficiency. Tight glass doors and better damper & draft controls can roughly double that, but both produce gia-normous sooty-particulate output. An EPA-rated fireplace insert with a nice glass door for viewing can hit north of 75% efficiency (with or without a noisy blower for distributing the heat and boosting peak output). If you're heating even partially with wood, it's far better in terms of total fuel use and your local air quality (including your homes interior air quality) to use a wood-stove or wood burning insert. Burning wood in an open hearth is at least as expensive as heating with oil, but burning wood in an insert or woodstove is quite a bit cheaper, even at $300/cord (typical central MA pricing for decent split seasoned hardwood, delivered.)