You may see it occasionally. English-speaking Russians often use "hehe" to show amusement, because it sounds a lot like the Russian equivalent, "хехе." Many professional translators, when translating from Russian to English, will use "hehe" to translate "хехе," in novels and other media. But native English speakers rarely use "hehe" themselves.
I agree with Irene's answer. "Haha" is fairly common, and the most common way to express laughter online or in text messages is "lol" ("laughing out loud"). I personally also use "heh," as Irene describes it (a mildly amused sound), and sometimes "hah!" if I'm more amused. I'm not sure if I qualify as an "older" speaker, but I do think of "lol" as a term that should be used only in extremely informal contexts. "Hah" or "heh" can be used in less informal situations.