Homeomorphism groups as topological groups

Question

As is well known, the homeomorphism group of a compact Hausdorff space is a topological group. The same is true for locally compact locally connected Hausdorff spaces, but it is false in general. Now what if the space is compactly generated and weak Hausdorff and the homeomorphism group carries the compactly generated topology stemming from the CO topology? Is it necessarily a topological group?