I don’t know the answer to your question (ie: does a regular cover over the screws effect tone?), but I do know Dimarzio has said covers for 12 screw pu’s. They’ll sell you the covered pu, but they won’t sell you a 12-hole cover to install it yourself. I called to buy one - no joy. Easy enough to add holes to a standard cover with some due care while drilling.
This is what im saying if a took a regular humbucker pickup like the photo im showing that would cover the bottom row of the hex pole pieces on the DiMarzio Super Distortion since it has the two rows of hex pole pieces so with the regular humbucker cover covering the bottom row of pole pieces would it effect the pickup differently, do the bottom row pole pieces have to be exposed
I'd be more worried about it fitting properly. I'd make sure to use some tape over the pole pieces being covered to ensure they don't resonate against the cover.
As for sound, yes, it'll affect the sound, but all covers do. They reduce highs to a small extent and might require lowering the pickup a small amount, slightly reducing the output.
I would get a 12 holer somewhere and put it on yourself. If you get the pole pieces up through the cover, it won't matter for the tone. Just put electrical tape between the cover and the pickup poles to prevent feedback from the cover ringing. I clamp it tight (with a rag on the clamp so you don't scratch anything) so the cover is tight before you solder it on, and then it's just a dab of solder in the corner.
I think if you don’t do that dip in wax thing it will be really prone to feedback. I had a LP once that feedbacked like crazy - my guitar guy said take the covers off. I did that and it was tons better - and it wasn’t wax potted