As directly quoted from the MissingNo. page on Bulbapedia:
"Missingno.'s appearance in-battle allows the item duplication glitch, which increases the number of items in the 6th Bag slot by 128 unless the number of items in the slot already exceeds 128.
Encountering Missingno. has been known to interfere with the save game data in various ways, such as adversely affecting the Hall of Fame saved data and (if its stats are viewed) messing with some graphics until the stats of a non-glitch Pokémon are viewed. When a Trainer battles with Missingno. in their party, both the Trainer sprite and their Pokémon's sprites will be scrambled, and all other sprites will be reversed. Viewing the stats screen of a non-glitch Pokémon will remove the effects.
In Pokémon Yellow, capturing Missingno. will cause multiple player sprites to walk around the screen. "
Nintendo has an official description of Missingno. listed in their Customer Service troubleshooting section. A direct Nintendo quote:
MissingNO is a programming quirk, and not a real part of the game. When you get this, your game can perform strangely, and the graphics will often become scrambled. The MissingNO Pokémon is most often found after you perform the Fight Safari Zone Pokémon trick. To fix the scrambled graphics, try releasing the MissingNo Pokémon. If the problem persists, the only solution is to re-start your game. This means erasing your current game and starting a brand new one."
TL;DR: No, it just messes with your save files, permanently messing them up, but not actually deleting them.