TLDR: Yes, it can happen at that altitude, but the odds are extremely low.
High-altitude cerebral edema has happened at lower than 10,000 ft.
The condition is seldom seen below 3,000 metres (9,800 ft),2 but in some rare cases it has developed as low as 2,500 metres (8,200 ft).
To give an idea of how rare those rare cases are, consider
HACE occurs in 0.5% to 1% of people who climb or trek between 4,000 metres (13,000 ft) and 5,000 metres (16,000 ft).
It's worth noting that while HACE is rare it also an extremely serious situation that will end fatally without treatment.
Although AMS is not life-threatening, HACE is usually fatal within 24 hours if untreated. Without treatment, the patient will enter a coma and then die. In some cases, patients have died within a few hours, and a few have survived for two days. Descriptions of fatal cases often involve climbers who continue ascending while suffering from the condition's symptoms.
The damage caused by HACE is long lasting,
"It was previously thought that HACE did not leave any traces in the brains of survivors," said Dr. Michael Knauth, PhD, director of the University Medical Center Department of Neuroradiology in Göttingen. "Our studies show that this is not the case. For several years after, microhemorrhages or microbleeds are visible in the brains of HACE survivors."
Survivors of the most clinically severe cases of HACE had the most prominent evidence of microhemorrhages on MRI, according to the research group. The bleeds were found predominantly in the corpus callosum, which consists of densely packed nerve fibers connecting the two brain hemispheres, and they showed a characteristic distribution different from other vascular diseases such as vasculitis.
For much higher peaks, their is a real risk of permanent brain damage and that is without showing signs of altitude sickness.
We recruited 35 climbers consecutively (12 were professional and 23 were amateur) in 4 expeditions without supplementary oxygen: 12 professionals and one amateur went up to Mt. Everest (8848 m), 8 amateurs to Mt. Aconcagua (6959 m), 7 amateurs to Mont Blanc (4810 m), and 7 amateurs to Mt. Kilimanjaro (5895 m). The mean age was 33.8 years (range: 22-46). All of them underwent general medical examination, standard blood tests, and MRI of the brain after the expeditions. MRI also was carried out in a control group of 20 healthy subjects. Single-voxel MR spectroscopy was carried out in 14 amateur subjects after the expeditions and in 10 healthy controls. As outcome measures, we evaluated changes in the hematocrit value, presence of cerebral lesions on MRI, as well as atrophy and dilatation of Virchow-Robin spaces, and differences in the metabolite ratios obtained from brain MRS in comparison with controls.
Only 1 in 13 of the Everest climbers had a normal MRI; the amateur showed frontal subcortical lesions, and the remainder had cortical atrophy and enlargement of Virchow-Robin spaces but no lesions. Among the remaining amateurs, 13 showed symptoms of high-altitude illness, 5 had subcortical irreversible lesions, and 10 had innumerable widened Virchow-Robin spaces. Conversely, we did not see any lesion in the control group. We found no significant differences in the metabolite ratios between climbers and controls.