I have a good friend, a longtime friend, who works at Microsoft now. He's one of the funniest people I've ever met, and among his schticks is a faux-hip one, in which the persona goes around saying, "Hey, I can dig that!" He happens to be a fabulous musician, so ironically, when it comes to music, he can play things that are genuinely diggable, even as, in one of his comic personae, he mocks the "cool" white bourgeois dude who's tragi-comically "hip."
I do wonder the extent to which "dig" is filially linked to the term "groove." One gets in the groove or finds something groovy, just as one digs or digs into an experience, but can one dig a groove? Hmmm. Perhaps one shouldn't use "one" when writing about "dig"--speaking of tragi-comically [un]-hip.
"Can you dig it?" is a rhetorical expression, although I believe in a tune by the group Chicago ("Saturday in the Park," if memory serves), the question is not treated thusly. "Can you dig it?" is followed by "Yes, I can." Chicago produced a great sound there for a while, but even from the beginning, the group was a bit nerdy. Nerd rock.
Anyway, here is a wee riff on the term "dig it":
When he said, “Dig the well,”
He wasn’t speaking Jazz or Beat
Or asking you to move your feet.
He meant shovel, and he meant hole.
The water-witching’s done, son.
Find that water-table,
If you’re able.
Dig the well good. Get it done.
It is not to my credit that I couldn't resist writing "Dig the well good." It amuses me, but I do apologize. Can you dig it? Don't answer that.