As far as we can figure it, basically, yeah. Wrapping your brain around the concept is less tricky than you'd think.

So gravity gets stronger the closer you are to a black hole, but at the event horizon things get weird. The extreme curvature of spacetime forces space itself to flow toward the singularity at its center faster than the speed of light, so on the inside there's no "other" direction to point to, even photons emitted straight "out" can't reach the event horizon and end up moving in the same direction as everything else. So space becomes timelike, proceeding inexorably from point A to B.

Time is more complicated, because it's really hard to visualize. If you fall into a black hole, you'll pass through all the outward-pointing light that's been failing to escape since the event horizon formed, which makes all the past history of the black hole visible below you. Meanwhile, anything that falls into the black hole after you can be seen falling from above as the downward-pointing photons catch up. The timeline of the inside of the black hole is laid out with the past and future being directions you can point to, making time spacelike.