The answer is no. Sorry, couldn't resist the temptation.
I see the connections, and I'd be just as happy to settle on "yes". For fun, here's where I could see a "no" coming from.
Seems to me that gag cartoons, and especially New Yorker and Far Side, tend toward an "auteur" vibe. You start with gag cartoons, and they're funny and people like them, but out of that certain schools and individuals "elevate" it to art. New Yorker and Far Side are representative of a genre but they're not just at the pinnacle - they transcend it. Not saying that's truth, but I believe that's a narrative. There are a lot of gag cartoonists, and they're great, then there's Larson. Like there are a lot of noir filmmakers and other folks making moody, offbeat films inside of Hollywood, and they were great, but then there were the art house directors who (supposedly) took that some of the themes and techniques to another level.
Maybe it's part of where gag cartoons come from - early to mid-century print culture.
If there's a link between single panel cartoons and memes, I think it would be in the familiar tradition of "caption this cartoon" contests. But that still feels very different. A newspaper might have done that to engage folks or even to find talent. I think that's a pretty big difference from the free flow we see with memes. The newspaper still selects the cartoon to caption, it's still done by a "professional".
At the end of the day, I don't know that we can get away from the fact that one person, who is supposedly talented or professional makes the key element of the single panel cartoon which is still the image. And that's pretty important. Even if a gag cartoon can be shared in ways that are similar to memes - "that 'Family Circle' cartoon perfectly encapsulates some cliche about family life such that thousands of people clip it out of the newspaper, mail it to their friends and they all put it up on their fridge or in their scrapbooks" - does that even become a "vocabulary"? Do we ever think of gag cartoons as constituting a set of visual symbols? that seems like an important part of memes. One last variation on this theme: seems pretty important that memes have a subversive element almost always - taking an image out of context to play up the humor in it that might not have been intended by the creator, captioning the image it different ways. Dissonance seems pretty important for memes where harmony is pretty essential to great cartoons. One way of talking about Larson or great New Yorker cartoonists would also fit a familiar narrative from "art" - they seem surprising even dissonant at first, but people ultimately find the harmony and the ways they continue the tradition and enrich it more than they subvert it. Seems like memes are only memes if there's constant dissonance and subversion (whether positive or negative in meaning or impact).
understood that none of this is really a "no". there are obviously a lot of similarities between gag cartoons and memes. I'd suggest that memes have other sources:
Ads (both commercial and political/propaganda) - I think a meme is a lot more like an old ad where the tag line and the illustration/photo are ridiculous and/or pathetic in their reality vs. the obvious (painfully obvious, usually) intention of the maker. Also ads tend to have regional differences such that lots of people experience seeing a different picture for the same ad when moving from one part of the world to another, etc. Or you see the tag line translated into different languages and that's funny. (I always like that when you translate the French version of "Finger Lickin' Good" back into English it's "So good, it makes you want to lick your fingers").
Badges/flags/money - these often combine an image and a motto, and they're often satirized by changing up the motto and/or the image
I like these two examples because it seems to me the traditions of expressing bemusement or outrage at the source image are much more like what we see with memes. when someone alters (vandalize, whatever word you're comfortable with) a poster to give it a new tag line to play up how the happy-happy image of consumption is actually terrifying, you're doing something very much like putting your own caption on a meme. And I'd say that comes from the kind of motivations that lead you to do it, to who you're communicating to, to what you want those people to think. Like when you alter that poster, (let's imagine for a second this is coming from an anarcho-punk, anti-capitalist vibe to help visualize) you might be hoping to make someone who has never thought twice about capitalism to feel worried or confused, you might be hoping to signal to other anti-capitalists that you're around. Also, that ad is up in a million places. So you could see another very "meme" like activity - all anti-capitalists could vandalize it in different ways, but ways that might be inspired by seeing what others have done or there could be a specific way of altering it that becomes a symbol of a group or movement.
And this gets back to some of those key characteristic of memes - the flow of creation and distribution is decentralized, repetition and adoption can codify certain memes into recognized shorthand symbols.
So I'd hypothesize that lovers of cartoons like us see the ways that memes are like cartoons. I'd further hypothesize that to the extent that memes can feel like they go "wrong" (get negative, hurtful), we wish for them to be more like a new form of the cartoon tradition because we might like to believe that would mitigate negative tendencies.
But it's fun to question to what extent memes come out of newspaper single panel cartoons. Seems like their origin may lie more with other kinds of visual activity, such as graffiti.
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