Does consummate have a negative connotation?

No, "consummate" does not have a negative connotation. In fact, it's quite the opposite. It means "supremely skilled, accomplished, or perfect".

Here are some examples:

* "She is a consummate professional." (This implies she is highly skilled and competent.)

* "The chef created a consummate meal." (This means the meal was absolutely perfect.)

Sometimes, the word "consummate" can be used in a more formal or even archaic context, but it still maintains its positive meaning.