According to some studies, there is some evidence that the virus could cross the BBB. Is that is the case, does that mean that it would weaken the barrier allowing potentially neurotoxic drugs to enter the brain. Could this happen for example if the virus downregulates p-glycoprotein which prevents the uptake of drugs?
An example of this concern is with the drug ivermectin which has gained some recent notoriety as a possible prophylactic and treatment of the infection. There is some evidence for the neurotoxicity of this drug in dogs.
 Rhea, E. M., Logsdon, A. F., Hansen, K. M., Williams, L. M., Reed, M. J., Baumann, K. K., ... & Erickson, M. A. (2021). The S1 protein of SARS-CoV-2 crosses the blood–brain barrier in mice. Nature neuroscience, 24(3), 368-378. https://doi.org/10.1038/s41593-020-00771-8 [Open Access]
 Merola, V. A., Khan, S., & Gwaltney-Brant, S. (2009). Ivermectin toxicosis in dogs: a retrospective study. Journal of the American Animal Hospital Association, 45(3), 106-111. https://doi.org/10.5326/0450106
Free copy at http://jcore-reference.highwire.org/content/45/3/106