Does 'droll' have a negative connotation?

Solution 1:

By and large, on the whole, not to put to fine a point on it, 'Very droll' is in itself, as far as one can tell, one of those phrases that speaks clearly its own meaning, when put into the context of the conversation that proceeded the remark.

When the tone of voice and body language are taken into account, one can tell quite easily the spirit in which the phrase was meant.

Solution 2:

Droll came into English from the French drôle and it arrived as a noun meaning:

A funny or waggish fellow; a merry-andrew, buffoon, jester, humourist. (OED).

The OED has no examples of its use since 1876, by which time it was clearly accepted as an adjective:

a1876 G. Dawson Biogr. Lect. (1886) 94 Charles the Second certainly was the drollest idol ever nation set up.

A more modern interpretation is available in the Oxford Dictionary Online. Clearly the adjectival use is now more important.

Curious or unusual in a way that provokes dry amusement: his unique brand of droll self-mockery.

In short to describe a remark, or someone as droll would imply that they have a sense of humour which is not especially quick witted.

So in answer to the question it is negative in the sense that it suggests the speaker, or the remark was an example of dry-wit, not especially funny. (Though I very much dislike the use of the term negative in this sort of sense. Reducing people to positivity and negativity suggets that they do not exist outside of a bi-polar spectrum.)