Anime, as a cartoon, appears to be a simpler drawing style than traditional drawing. Therefore, it would seem to be easier to learn to draw in the style of anime rather than traditional. However, anime is not exactly a simplified version of traditional drawing, but rather a stylized version; all drawing styles share the same basics and therefore anime drawing basics are the same as traditional drawing basics. This follows the idea of any area of skill: you have to know the rules before you can break them.
The absolute basic first step of drawing, any drawing, is breaking down the desired object into basic shapes: circle, square, triangle, trapezoid. For living creatures, a line of motion is also essential; this line represents the positioning of the creature, incorporating what action the creature is performing.
Typically, the line of motion is drawn as the spine of the creature; that is to say, a circle, generally, is sketched to place the head, and then a line denoting the spine shows the movement of the creature. This clearly has its place in anime as much as traditional drawing, perhaps even moreso as anime characters, as cartoons, often have more severe and unlikely movements than other styles of drawing. Without any skill in this basic aspect of drawing, the anime characters are likely to come out misshapen and stiff. While the misshapen aspect may be more kindly overlooked in an anime character, this style of drawing is one of the most loose and limber.
Learning traditional art in drawing humans forces the artist to learn how to draw human emotions as they are expressed through actual facial movements. While anime, as a highly stylized art form, has rather iconic ways of displaying these same emotions, the quality of the anime will improve vastly if the artist has the ability to capture human emotions through movements of the eyebrows, eyelids, lips, cheeks, and nose, which traditional art requires. In beginning drawing, typically only the eyebrows and lips are used to express emotions and while this is a great start, to improve the artist should realize that at the very least, eyelids should be considered as these dominate most human expression; in anime, eyelid movement is typically marked by the size of the eyes themselves with eyelids being semi or non present.
Finally, dimensions in living objects are critical to a viewer's recognition of the object. Human dimensions are a little tricky due to the fact that actual human beings may be disproportional, but the variation is usually not so great as an amateurish mistake from lack of knowledge of these proportions altogether. As anime is stylized, anime proportions are directly a result of breaking a rule after mastering said rule. No artist can hope to consistently draw anime characters with proper-looking bodies without having at least some grasp on actual human proportions and the ability to draw them realistically.
This is especially true for chibi style, as an extremely stylized rendition. Typically chibis have a body size half the proportional size it should be, and perhaps engorged heads. This means that arms are typically half-length, proportionally - that is to say, if the chibi were to raise its arms up, its hand or arm stub as the case may be would reach the level of the top of the chibi's head, as opposed to a real human whose elbow would reach around the top of the subject's head. Understanding dimensions is usually accompanied with understanding movement and movement, as explained, is critical to anime where characters are often more free-flowing and/or active.
Thus, the basics of traditional drawing serve as anime drawing basics as well, and learning even a little traditional drawing will improve an artist's ability to create anime.