Can I connect the R and C wires directly to the HVAC transformer?
Based on the ladder diagram, it looks like the R terminal is only energized when all the limits (main limit and however many rollout limits there are) are closed. So if any of the limits open, the thermostat loses power (maybe).

I can't say for sure; since I'm not familiar with that board, but if that's how the furnace disables itself during a problem. Then bypassing that safety system can be quite dangerous.  I'm not sure if the board monitors the limit circuit, or simply cuts power to the R terminal in the event of an open limit.  If it's the latter, then connecting the thermostat directly to the transformer would be hazardous.

WARNING:
The following procedure requires working on energized equipment. If you're not comfortable with that, please contact a local licensed HVAC technician.


Connect the thermostat as normal, with the system powered on, and the thermostat not calling for heat/cool/fan.
Open the access panel for the furnace, and locate one of the limit switches.
Remove one of the low voltage signal wires from the limit.
If removing the panel cuts power to the system, replace the cover.

In this state the furnace will not work. But what you're looking for, is whether or not the thermostat has power.  If not, then you're not going to want to bypass the IFC. It also means that whenever a limit opens, the thermostat is going to reset. Which is not a terrible thing, as it makes it obvious that there's a problem with the furnace.

Right now the thermostat is connected to the IFC terminals like this.

If instead you connected the thermostat directly to the transformer, then it would look more like this.

You'll notice that the limit circuit (highlighted in red), is completely bypassed by connecting the thermostat directly to the transformer. Which means even if one of those switches open, the thermostat will still be able to signal for heat/cooling.
Again, I'm not familiar with this IFC, I'm simply basing this on the diagram provided.  The IFC may in fact monitor the limit circuit, which is why I recommend testing it.