I would say, yeah it's important. They didn't make it that wide to support the spare... it's part of your frame after all. Even if it's not technically necessary it's probably better to have something there-
I think you could safely get away with putting support plates in place of it... if your underfloor storage is supported in the van floor (angle iron?) marked in red, cut beyond that in the frame (since the frame and body move independently) and put support plates from the two sides of the frame to replace the missing section. In addition to possibly needing this support, you can feel more comfortable cutting the whole underfloor storage a little wider instead of just fitting it between the frame pieces.
Wait, back up.
First weld the two supporting plates in blue to the frame, THEN cut for your underfloor storage.