After I download an application (or a disk image or zip file containing an application) with either Firefox or Opera, and try to open it, Mac OS always asks me if I'm sure, because it was downloaded from the Internet.
I'm not so sure if the level of support is the same -- for example, when downloading with Safari, this dialog often shows the URL where the application was downloaded from. I rarely (if ever) see that information with Firefox or Safari. Thankfully, these are test that you can easily perform yourself if you are curious about the level of support.