Most are, but not all.
The answer is definitely yes in the case of a glitch like wall clipping in Super Mario Bros. A simple glitch like that is an unintended result of ordinary gameplay code which, unless specifically altered, will be faithfully reproduced by the emulator.
There are so far no know examples of Nintendo fixing glitches like this (intentionally or unintentionally) in any of their Virtual Console or Classic/Mini console emulators. Things that have been changed in the emulated re-releases include consistency fixes for regional version differences, reductions in bright flashing colors to reduce the risk of seizures, and occasional minor graphical cleanup (examples).
Where an emulator might not faithfully reproduce a glitch is where it involves the low-level hardware. Many NES and SNES games have glitches/crashes which behave a certain way because of the memory and processor systems specific to the console. Emulated re-releases may exhibit different behavior when such a glitch is triggered, may crash where the original hardware didn't (or vice versa), or may be unaffected by the glitch altogether.