To my knowledge no, nobody has specifically studied this in relation to COVID-19. I can't really prove the negative but I tried a few combinations of search terms in to PubMed and came up with nothing.
The "Hot Toddy" (with varying exact recipes) does however have a long history as a folk remedy for cold and flu symptoms and you'll often find many people willing to provide subjective anecdotes about how it always makes them feel better.
So is there anything to it?
A paper in Rhinology Journal describing a pilot study published in 2008 looked at whether drinking a hot beverage versus a cold one had any effect. They looked at both objective measurements of nasal conductance and subjects' subjective evaluations of the severity of their symptoms (runny nose, cough, sneezing,
sore throat, chilliness and tiredness).
While there doesn't appear to have been any measurable improvement in the nasal conductance - the subjective results were more promising:
The results demonstrate that a hot fruit drink can provide subjective relief from all the six symptoms of common cold that
were scored in this study. Ingestion of the same drink at room
temperature only provided relief for three of the symptoms.
This demonstrates the extra benefit provided by the increase
in drink temperature and supports the traditional use of hot
drinks to relieve common cold symptoms.
The exact mechanism behind that relief is undetermined although there is speculation in the paper including placebo effect and some interaction with the major palatine nerve.
But heat is only one aspect of a hot toddy! What about the others? Well the lemon is going to give you some vitamin C - which is certainly good for you in general terms it's been a matter of consternation about it's usefulness when it comes to colds and similar illnesses. I'm not even going to begin to try and settle that particular argument. Here's a modestly-sized study in Nature that says vit-C helps reduce the frequency of colds (but not the severity or duration) and here's a large systemic review from Cochrane says no reduction in incidence but some reduction in severity and duration with regular supplementation (but questionable benefit therapeutically).
The evidence for honey is clearer - a systemic review published in the BMJ suggests that honey is good - especially for cough-related symptoms:
The researchers analysed studies that compared the effect of taking honey, in forms such as teas, neat, or mixed with other ingredients, to either usual care – such as antibiotics, or over-the-counter cough syrups and medications – or medically inert placebos. Studies compared symptoms such as cough severity, cough frequency and symptom length.
They found that, compared to usual care, honey was associated with a significantly greater reduction in symptoms, specifically cough severity and frequency.
Finally.. the whiskey. The alcohol is potentially going to have a small dehydrative effect and can suppress immune activity. So the whiskey is unlikely to be doing you an actual good - but I suppose it might cheer you up if you're a little buzzed.
Now, all of this has been about the various illnesses that all get grouped together under the umbrella of "the common cold". COVID-19 is caused by a coronavirus called SARS-CoV-2, some "common colds" are caused by other coronaviruses but most are caused by rhinovirus, so same symptoms: different cause (hilariously getting a rhinovirus might actually protect the host from SARS-CoV-2). So does any of this prior research matter for the Hot Toddy going up against COVID-19?
Only in so much as if the subjective relief of "cold" symptoms holds for their analogs in mild COVID-19 infection - the honey might help with the cough etc. Not even the most wildly enthusiastic claims about the medicinal properties of the hot toddy have ever suggested it can do anything about the more serious symptoms of a severe COVID-19 case - pneumonia and so on.
And there's just nothing there to suggest that it would prevent COVID-19 or that it would actually treat the infection so I'd have to say that's why you haven't seen any "Hot Toddy as treatment for COVID-19" studies and you're not likely to either.
You might see some studies on the effectiveness of home-care treatments for mild cases later on - as academic curiosity if nothing else. But in the current situation - where you've got a serious disease doing serious harm to many people globally the focus us rightly on treatments for severe cases, and there's just no real reason for the scientists and doctors doing that to say "You know what Jim - my gran always swore by a Hot Toddy when she had a cold, shall we give that a go?"
