Can I add a non-E.164 number to a phone field for an External Contact?

You can use the Other phone field.

To add non-E.164 numbers, or numbers that do not conform to the international telephone numbering plan, do the following:

1. From the country flag list, click No country code .
2. Enter any combination of letters and numbers.
3. Continue adding or editing the contact record or click Save.
   Note: Non-E.164 numbers are not searchable.