Such spray [0] has been on the market by multiple brands and is backed by studies [1]. It has a throat spray and lozenges, too. There are some other patented variants with a different type of carrageenan.
One study during the pandemic which showed efficacy which could control for use by targeting healthcare workers in their workplace: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8493111/
[0]: https://www.boots.com/boots-dual-defence-nasal-spray-20ml-10...
[0]: https://www.carragelose.com/en/portfolio/common-cold-product...
[0]: https://www.carragelose.com/en/portfolio/launched-products