Maybe I'm confused about what you are asking:
For an initial weld, you are correct, you can wick the solvent into the gap, and as long as the joint is firmed up so that the pieces are touching while it cures, you will have a sealed joint.
What appears to have happened is that you did not have a tight fit on this joint, so air intruded into the joint. What I do is set up the horizontal panel on a surface that is covered with compressible foam so take out the irregularities in the thickness, add the solvent, then add weight to the top of the assembly to make sure air doesn't intrude.
I thought what you were asking was related to adding solvent AFTER this was done - meaning, to the existing piece, after it was found to be leaking. If this is indeed what you are referring to, the issue is that once you have a bonded joint that is leaking, you can't "un bond" the joint just by adding solvent - there is not enough time for the solvent to dissolve the joint, because all you need for a joint to not hold water is one tiny pathway. You can seal off this pathway with repeated treatments of liquid thin solvent, think of it like painting on layers. Each application dissolves and liquifies a bit of material, so repeated applications should eventually seal up the gap well enough. The gel type solvent - weld on 16 - does this a bit better. #40 is a gap filler and one bead on each inside joint will seal it for sure.