Yes, probably.

1. If it's only the one screw holding it in place, I'd check the box to make sure it was firmly seated against the joist and wouldn't wobble.

2. I don't think the box complies with code as is: the front of it seems to be located about at the back side of the drywall. Code requires a box extender if there is more than 1/4" between where the front of the box is set and the face of the wall.

It looks like I can see the joist behind the box on the right. If it is, and it extends to the left also, I would drill holes through the back and put in two more screws. It also depends somewhat on the size of the fan, but I think that would work. Regarding the recessed box, you can get a box extender of the right thickness.

If the box isnt marked for supporting a fan, it isn't legal to support a fan. The fact that it's screwed into a joist is only half the issue. The box itself has to have mounting points that are strong enough to take the 35+ lbs of the fan.

"If the box isnt marked for supporting a fan, it isn't legal to support a fan."

"Are you positive that it's mounted directly to a joist?"

No, further examination shows that the electrical box is attached to something metal, perhaps a brace as you suggest. I'm going to remove the box and look inside the ceiling. If the brace is installed properly, I understand from a Q&A posted elsewhere that I can get a fan-compliant box and attach it to the existing brace (properly, not just with a big lug like the current box).

The fan I'm considering weighs 17 lbs.

That type of brace is not fan rated. You can get fan rated retrofit braces though that existing brace will be in the way.

With difficulty because it was nailed to the joists, I removed the old brace and box and installed a fan-capable replacement.