Very unlikely given what we know about biochemistry. Vitamin D is fat-soluble so your body stores it in fat.
Because of this, levels are generally stable over a period of months. Although there are health conditions that cause vitamin D levels to fall (particularly chronic kidney disease), it's highly implausible that COVID-19 itself could cause vitamin D deficiency directly.
Even if COVID-19 were to cause kidney issues and you didn't see sunlight for two weeks, it wouldn't move someone with adequate vitamin D levels into the deficient range. The time period is simply too short.
It's a correlational study, so that'd be difficult. Although an experimental double-blind study was posted here a couple of weeks ago that had impressive results.
