I always hesitate to use the term "any" in this context since there might be exceptions. But yes the red-mediated recombination system works in many other gram negative bacteria. However the plasmids designed to do this in E. coli will not work in most other gram negative (except for close relatives of E. coli) so you need to find appropriate plasmids for your host. Having said that, many non E. coli hosts do not need the Red system in order to do this type of recombination, it depends upon their intrinsic recombination enzymes of the host.

In other words it very much will depend upon which bacterium you are working with.