Yes but it doesn't go into mega combustion and can be damped down without significant impact to structural integrity if caught. I suspect that the bales used were not properly co.pacted for building. Unfortunately there is little regulation in this sector at the moment.
I don't think you have any experience of this sort of fire.
I have. With hay stacks and compacted organic matter. Memorably a grass fire catching on old compacted sawdust and soil.
When fire got into old (extremely compacted, consistency of peat) stables manure diggings, it took several weeks for it too breach the surface. It had briefly, for maybe 2 minutes, contacted the surface of the old stable sawdust and soil before being spotted and saturated with water. Several weeks later fire breached the surface of the ground 6 feet away. It took days of soaking with water to put that out.
If the straw bales are very densely compacted and there is suspected fire penetration, you couldn't simply dampen down. You would have to remove the bale structure to a significant amount back from the affected point to be certain there wasn't any combustion taking place.