I'd certainly do the sump, a lot of pattern panel people do sumps as well like Hadrian.
It may well be the case that owing to the bodge the car suffered oil loss which has caused some crank/shell wear and that is why the light is on at tickover.
It would be wise to do an oil change and flush too.
If it is only on at tickover I would just put up with it, otherwise you will spend a lot of money on a rebuild when you could have many thousands of miles yet from this engine.
I have had cars that took 10 seconds for the oil pressure to build enough to stop the knocking before now, and still had a fair few thousand out of them, the old triumph sixes were famous for this, from new, as oil draine dback from poorly designed system but still would do over 100,000 miles.
tabetha