Assumptions
A lot of assumptions being made here:
For example I'm not sure where it states that the aircraft was not VFR at all times - when public transport would be perfectly legal in a single. Also, given the reported name of the operator includes Pacific, last time I looked Ireland does not have a Pacific coast and the aircraft is "N" reg - perhaps an American company operating under a FAA AOC? Also, I'm not current on air law - particularly FAA and changes since EASA - but rule of thumb used to be two out of three make it legal (registration, licence/AOC, location) - so a pilot with an FAA IR flying an N-Reg a/c on a US AOC would have been OK - even IMC under some circumstances [I recall that last time I looked some years ago, night and IMC for public transport in Cessna Caravans was on the verge of being approved in the US/Canada].
Also, perhaps one of the engineers chartered the aircraft under a self-fly hire arrangement and then separately contracted the pilot to fly it for him - a grey area admittedly but an awful lot of aerial work is not, in fact, public transport.
Having said all that, the IAA to my certain knowledge, take a pretty dim view of illegal public transport, so I hope the pilot, his employers and the a/c owners have all their ducks in a row!
Unless suicidal, why would the pilot have flown on if he was aware? If the pilot was aware, very probably so would his passengers be. It would be a bit of a coincidence that all were suicidal at the same time. If they all were, why divert when their mutual oblivion was coing within reach? No, they patently did not know the extent of the damage.
As well as losing the lift from the missing part of the wing, the weight of the auxiliary fuel tank would be lost - ofsetting the lift imbalance. The increased form drag from the mashed up metal at the end of the port wing might be offset by the reduction in induced drag - hence decreasing the amount of rudder trim required to keep it all in balance.
Never never underestimate human factors and our ability to convince ourselves that everything is allright.
"(Very) loud bang, very close to tree tops on a take-off that was perhaps ill-advised - but everything still seems to work (fuel guages not checked yet, but then the engine had only been run for a few minutes). Maybe a little sluggish and unbalanced on the controls, but within "normal" tolerances - might be due to uneven loading due to size & distribution of pax and their gear. Yeah, everything seems OK. Phew, looks like I got away with the takeoff, must have been a bird. Press on"
Lucky, lucky people! Seems likely that a similar "oh I'm sure they have everything under control" scenario may have had the cabin crew of a Helios 737 continuing to sit in their seats when their a/c recommenced a climb having already deployed the pax oxygen system - by the time they found the hypoxic pilots it was already too late and the results were tragic.
The lesson for me from this is "just because it looks OK from where I'm sitting doesn't mean it is" Pilots that live to be too old to fly make conservative decisions and never, never assume the best. If you hear a loud bang, you need to establish what caused it and what it has done. If there are bits you can't see (and there always are) get someone else to check those bits out. I'm not sure I would "test the envelope" either. Supposing slow speed checks reveal an aerodynamic fault you can't recover from. Keep it flying as close as possible to the speed and configuration its already in (after all, it's staying up like that). In this case, a short flight without touching trim, undercarriage and flap controls unless absolutely essential) and approach to a nice long strip with good emergency services (such as Shannon) would seem to be favourite.