It will work, with all the disadvantages of solderless breadboards + distortion from soldering unsupported header pins + fragility from relying on glue to keep the header strips together. You can build it once, but if you need to modify or repair the assembly it will be an absolute nightmare. There's also no good way to mount it - at least real breadboards and stripboard can be screwed down.
If you need denser construction than can reasonably be constructed on stripboard, and don't want to make a PCB or do a 'dead bug'/'Manhattan island' build with SMD parts, consider matrixboard (one pad per hole protoboard), which with point to point wiring on the copper side is only larger than your idea by the thickness of the board + any extra area you allow for mounting holes.