Should be, and it looks like you put the wire on the screw rather than into the back, so no reason they wouldn't be sharing the hot then.

Since it's a light: is the bulb dead? Is there something going on at the fan end that you need to look at? If you're positive you have the hot correct then what you have is what should work. If the light is still out, look elsewhere.

You mentioned elsewhere a remote for the fan, so really you don't want the fan off a switch, you want it always live so the remote works. (Assuming you plan to use the remote) in which case you would just wire the fan line directly to the hot and install a single switch between hot and the light.