I believe that the facts may differ as to that interpretation.
Once and for all, by every definition from linguistic to clinical, Churchill was not an alcoholic, nor even an excessive alcohol consumer.
winstonchurchill.hillsdale.edu
Mr. Churchill began the day with a scotch and soda so watered down as to be on the level of mouthwash, followed by another before lunch
Alcohol result: Barely statistically noticeable
Lunch: 1 imperial pint of champagne and an ounce of brandy
Alcohol result: 5 standard drinks for the champers + 0.75 standard drinks for the brandy
Dinner: 1 imperial pint of champagne and an ounce of brandy (substitute claret for champagne in some cases)
Alcohol result: 5 standard drinks for the champers + 0.75 standard drinks for the brandy
Other: Further 3-4 scotch and sodas through the day and evening
Alcohol result: Barely statistically noticeable
Combined with this schedule of drinking is 3 decent sized meals and a late afternoon nap of a couple of hours.
The result, or approximately 12-14 standard drinks, is enough nominally for someone to be a bit more than buzzed, but spread out over an entire day from 1030-0200, with three decent sized meals, barely approaches that.
An average non-drinking chap of a decent BMI will likely get 'buzzed' off 2-3 standard drinks, but someone used to drinking will usually take 5 standard drinks in an hour (~2 imperial pints of beer) to start to feel anything. To actually get pissed, call it double that.
In terms of legally intoxicated, or 0.08% on various US and Australian standards to use an example, he'd be there after lunch and dinner by virtue of recent booze intake, as even food doesn't change that in biochemical terms. However, he never drove in any case, let alone going for a bit of a flex after dinner when he'd had a skinful.
Given that an imperial pint of beer (583ml) is ~2.3 standard drinks, the notion of 'buzzed' is very subjective. A very thin chap, which Churchill wasn't, could get 'buzzed' off one if he drank it quickly. In a decent sized bloke who is used to drinking, it won't touch the sides.
(1 standard drink = 10 grams of alcohol)
Long story short: If there were breathalysers back then, he'd probably register. But I don't believe, on the balance of evidence, that he'd be substantially pissed or even buzzed, save for a very ephemeral period directly after lunch or din-dins.