Probably not: but nobody knows for certain (which is mind-boggling to me, given that the field of computer science is relatively new). Let me tell you what we do know:

Cookies on the web, more-correctly known as HTTP Cookies, are a specific type of cookie, but cookies for this purpose predate the web. They’re almost certainly named after Magic Cookies, which are a more-general computer science concept but fundamentally similar: a piece of data that gets passed backwards and forwards in order to identify the processes at one or both ends of a connection. From there, the trail gets colder: it’s possible that Magic Cookies take their name from the “cookies” that represented the end goal of compilation in some C compilers, as hinted at here (these, in turn, were probably so-named because when you’ve achieved something… you probably deserve a cookie). Or it may be related to a particular class of early malware and/or hacking tools that saturated your connection with “I WANT A COOKIE” messages until you typed “COOKIE” back to it, which were in turn related to Sesame Street’s Cookie Monster, although this article suggests that the term predates Sesame Street and relates instead to a 1960s cereal with a “cookie bear” mascot. Or it might relate to the term “cookie jar”, which some operating systems use internally to refer to the location in which configuration data are stored (although I can’t find any evidence that this was the case prior to the earliest uses of the term “magic cookie”). Some folks claim that it’s a reference to cookies in a 1976 computer game called Colossal Cave Adventure (or more-often Colossal Cave or just Adventure), although it’s certainly the case that no contemporary version of the game contains any mention of cookies. Other folks claim that it’s somehow related to fortune cookies.

In short, we don’t know. But it’s probably got nothing to do with a “crumb” metaphor, as HTTP cookies don’t by-themselves leave any information where they’ve been (and earliler magic cookies even less-so).