That works two ways.
A larger amount can make it trhough from top to bottom,
And, and I was goint to post about this, OP is there any chance your downspout is partially clogged? I'm not sure how to find out. If it were totally clogged, a garden hose from the top to the bottom with water pouring out might dislodge a clog. Maybe separate the straight part and look from one end to the other.
My AC has a pipe from the evaporator coil, the A-coil tray, to the sump, and everythign was fine the first 10 years I was here. Then I found water coming out the bottom of the furnace. Figured out it was condensate that was overflowing the tray. Cut off the plastic pipe and ran a garden hose from the laundry sink to the open piple and water poured out into the sump. Didn't seem like it was ever clogged but certainly wasn't now. Glued the pipe back together again. Same problem.
Pipe came out of the A-coil area, went down 1 inch, over to the wall, down theto the floor, and over to the sump. I rearranged it so it went down 6 inches at first, instead of 1, and everything worked again. No overflow. I have no idea why but it reminds me of your gutters.