Short answer: yes
Long answer: no
Brain fog is associated with the symptoms of "slow thinking, difficulty focusing, confusion, lack of concentration, forgetfulness, or a haziness in thought processes" (Ocon 2013). Many people may experience these symptoms on a daily basis. However for a case to be considered as Chronic Fatigue Syndrome (CFS), which is where the term "brain fog" derives from, a patient must experience fatigue for a minimum of 6 months and "at least four of the following symptoms must be concurrently present: pharyngeal pain, cervical or axillary lymphadenopathy, myalgia, polyarthritis without erythema or edema, headache, non-restful sleep, prolonged post-exercise fatigue, and/or debilitating cognitive impairments in short-term memory and concentration" (Fukuda et al., 1994). While many people will experience some of the symptoms of brain fog throughout their life, if brain fog is chronic and affects daily life then there is more going on than just purely caffeine consumption.
Overconsumption of caffeine can lead to insomnia and migraines which are 2 out of 4 conditions required for CFS (Saimaiti et al., 2022). Consuming up to 400 mg of caffeine per day has not found significant results in leading to a reason of overconsumption, however a time dependence for a consumption window at least 6 hours before sleeping was found (Saimaiti et al., 2022).
The most common can of Celsius has 200mg of caffeine, and you would need to drink more than 2 full cans per day in order to be approaching levels of overconsumption. It's also important to note that consuming caffeine 6 hours before bed can cause non-restful sleep, which has its own implications. The claim that Celsius directly causes brain fog is misleading. The originally referenced article in claim also concluded that Celsius is still viable for the average person given they are already living a healthy life and have the added caffeine with their "budget" (Jamie N 2023).
Ocon, Anthony James. “Caught in the Thickness of Brain Fog: Exploring the Cognitive Symptoms of Chronic Fatigue Syndrome.”
Frontiers in Physiology, vol. 4, Apr. 2013.
Frontiers,
https://doi.org/10.3389/fphys.2013.00063.
Fukuda, Keiji. “The Chronic Fatigue Syndrome: A Comprehensive Approach to Its Definition and Study.”
Annals of Internal Medicine, vol. 121, no. 12, Dec. 1994, p. 953.
DOI.org (Crossref),
https://doi.org/10.7326/0003-4819-121-12-199412150-00009.
Saimaiti, Adila, et al. “Dietary Sources, Health Benefits, and Risks of Caffeine.” Critical Reviews in Food Science and Nutrition, vol. 63, no. 29, Nov. 2023, pp. 9648–66. Taylor and Francis+NEJM, https://doi.org/10.1080/10408398.2022.2074362.
Dietitian, Jamie N., Registered. “Is Celsius Bad for You? The Truth from a Dietitian.”
The Balanced Nutritionist, 9 Aug. 2023,
https://thebalancednutritionist.com/is-celsius-bad-for-you/.