Plenty of fans and non-fans are able to correctly tell the difference between anime and non-anime when it is presented to them, typically within the first minute (second?). This indicates that there is in fact a dimension to the artistic style of anime that is consistent across the entire collection of works. This artistic dimension, whether in pacing, character design, set design, artwork, sound, plot, characterization, or animation does exist, whether or not individuals can identify or agree on what the elements are.
That said, I do not believe that D&D contains these elements. Certainly some elements, such as animation, can't possibly be included in the game. Most of the other elements, though, are artistic in nature, and not codified in the ruleset, or even codifiable. It is possible for the artwork in D&D to contain a number of anime elements, but I haven't seen any evidence that WOTC has included them in artwork. Indeed, it appears that WOTC has deliberately made sure that official D&D art does not contain these elements, keeping it artistically distinct and non-anime in style.
So, I don't think that D&D is anime-influenced.