A board bow can survive with grain run offs. Lower weight bows survive them better. The angle of the run-off generally determines how much a problem they are. The steeper the angle the more likely they are to break. Also, the different types of wood are more likely to survive growth ring violations (which is what a runoff really is). Red oak is not a wood that tends to survive with significant grain run offs.
If the board you showed us if flat sawn or plain (not rift sawn) I think you should look at the edge grain. The run offs on the edge grain are what represent growth ring violations. However when the back grain moves from one side of the board to the other this generally means you will have grain runoffs on the edge.
The board you showed will have pretty decent run-offs. It could survive without backing, depending on how "high stress" the design is, but those runoffs are a big liability. Backing a board bow with runoffs (in my experience), with a low stretch fabric such as linen or silk, can greatly improve its safety.
Id say, keep the bow long (68") and a bit wider than usual, and keep the weight under 50lbs. But given the option I'd back it with linen.
Gabe