Well, regarding compatibility with Sturmey-Archer, things aren't good. To start with, whatever mechanism that hub uses to operate the internals (probably a pullchain) is unlikely to be compatible with a Sturmey-Archer one, simply because the threading will be different. SA axles are also an unusual whitworth thread, which that hub is unlikely to share, meaning you probably won't even be able to use SA axle nut with the tall section for the pullchain to route over. As for compatibility between internal parts, you're probably out of luck.

One issue with the earlier SA 3-speed coaster brake hubs was that the brake was operated through the gear train, meaning that a) it was less powerful in high gears, when the bike would be moving faster and b) if the gears weren't adjusted correctly and didn't engage properly, the brake didn't work. I don't know how the SRAM hub works, but it may have the same issue.

As always, you have got a front brake as well, haven't you?