Not implausible, similar RCTs exist for other nasal sprays ( But it would be important to know how many hours after application of the spray viral load was measured). This is for iota-carrageenan from a month ago, and widely available in some European countries.
“In the multicenter, randomized, double-blind, controlled CARR-COV-02 study, 394 healthcare staff were randomly assigned to receive iota-carrageenan nasal spray (N = 199) or placebo (N = 195) four times per day. [...]The percentage of participants that developed COVID-19 was significantly lower in the group that received the iota-carrageenan spray compared to placebo (1.0% vs 5.1%, respectively; relative risk reduction for disease of 80.4 %; 95 % CI = 25-95 % ).”
But it would be somewhat surprising if it were to protect you from complications once you are actually infected, as viral load in the throat or lungs would not be reduced.
It might help if you have an infection in your nasal pathways to prevent that infection from spreading to other body parts.
Yes, but only if you do it early enough. By the time you are PCR positive I would assume it is already too late.
Yes. Maybe it still manages to reduce the amount of COVID-19 in the nose (and that’s what the standard PCR tests measure) and thus would produce a false result.