Does the metaphor "Swiss Army knife" have a negative connotation?
The Swiss army knife has, presumably, a huge array of tools -- way more than most people would need. In other words, it's overkill. See, for example:
Folks who want a true do-it-all tool will appreciate this knife, but it's really overkill for most campers. (source)
Others have used this overkill way of loading something up with features in an absurd way as a metaphor, for example this rant about the smart phone:
The cork-screw, the scissors, the magnifier, the golf club cleaner, and the wire cutter in a Swiss Army knife are OK, but they are not the best tools for doing the respective jobs. Wireless phones have become the Swiss Army knife for communication, networking, and entertainment. (source)
It's reasonably common.