So, would some, or more, TNG special effects need to be remastered for HD?
ALL of the effects would need to be redone from scratch.
This is because all EFX were done on videotape; the highest resolution possible is 480i. It's simply not possible to show that in HD.
The live action scenes can be shown in HD, because they were shot on film, and the native resolution of film is much higher than even HD. But all the effects would have to be done anew.
This is also true for DS9 and Voyager. (Only ENT is airable in HD 'as is')