Is it possible to transfer MissingNo. and other Gen 1 Glitch Pokémon to the PokéBank?

That's not true you can't transfer anything from first generation games to Pokémon Bank.

According to Pokemon.com:

Once Pokémon Bank has been updated, you'll be able to use it to transfer Pokémon you've caught in the Nintendo 3DS Virtual Console versions of Pokémon Red, Pokémon Blue, and Pokémon Yellow into your copy of Pokémon Sun or Pokémon Moon.

EDIT:

Regarding your question, Mew could only legally be obtained in Virtual Consoles through an event. All Mew received from such an event have an OT of "GF" and an OT ID of "22796". If a Mew does not have these values, it won't transfer.
See this answer for further info.

This is also true with MissingNo, it is actually a glitch and not a true Pokemon.
I remember when I tried to trade it from Blue to Gold, the game recognized it as a Slowpoke showing me a message like:

Your Slowpoke has something wrong.

So I'm pretty sure you won't be able to trade MissingNo nor Mew (but only if its OT and ID differ from the event one).