Will a curtain tension rod support blackout curtains?
Most likely, yes. I've used a few shower curtain rods of similar design on painted drywall, and they do fine. Blackout curtains are not lead-lined or anything. In fact, they don't weigh much more than standard fabric curtains in most cases. I have some in my bedroom now and they're quite light.
If you install the expandable rod carefully and don't expect it to hold the heaviest curtains out there, it should work fine. If you find that the rubber pads are slipping against the painted wall, consider something like removable double-sided foam tape between for extra friction.
Keep in mind that you'll punch a hole in unsupported drywall with these if you get careless. Investigate first using a studfinder or a few knuckle taps and install accordingly.