Unlikely; Wolfram Alpha is based on Mathematica, which has arbitrary-precision integers, and I don't think one wolfram can be more than about 10^12 nano-dijkstras.
(If I put "1 wolfram" into Alpha then it tells me about Stephen Wolfram. If I put "2 wolfram" into Alpha it tells me about tungsten. I guess that when you ask it for "1 whatever", it first simplifies it to "whatever", and then you can have variable quantities of tungsten but not of Stephen Wolfram.)
Wolfram is also another name for the chemical element "tungsten" https://en.wikipedia.org/wiki/Wolfram_(element) ("2 wolfram" probably means "give me the second meaning of 'wolfram'"). Mathematica/WolframAlpha is probably not smart enough to figure out unambiguously how much mass or energy could be in one nano-dijkstra, which it would need for such a conversion.
On the other hand, referring to "1 wolfram", some would argue that one wolfram could greatly exceed 10^12 nano-dijkstras... Dijkstra was actually quite smart and from reading his essays, I'd consider him quite humble, not arrogant at all.
He had that "old-noble-European cold-joking-seriousness" and most Americans are known to be incapable of understanding this tone of communication.
(If I put "1 wolfram" into Alpha then it tells me about Stephen Wolfram. If I put "2 wolfram" into Alpha it tells me about tungsten. I guess that when you ask it for "1 whatever", it first simplifies it to "whatever", and then you can have variable quantities of tungsten but not of Stephen Wolfram.)