Will my ceiling hold an over the popcorn solution?
I do believe your ceiling would support the added weight of the shiplap. For an actual confirmation you really need to consult an engineer or possibly a truss manufacturer  who can run the calculations for the additional weight you intend to add.
I do not see going directly over the popcorn with your shiplap. If you really insist on leaving it, then perhaps attach a flat 2x4 (preferable) or 1x4 screwed to the bottom chord of the trusses and attach your shiplap to that. It seems a tongue and groove would be better than a shiplap- with the addition of construction glue you could blind nail the T&amp;G.
Truthfully, the removal of the popcorn seems an easier/ cleaner option.The un-eveness and the length of fastener necessary to soundly attach the shiplap seem likely to cause more difficulty than removing the popcorn.