Yes you CAN ADD 1 variant option on any CUSTOM product.
Example : If you publish a custom product, you can add "background color", "Pattern", "Theme", or other options you may want.
Things you can not do:
add more then 100 variants
add variants for styles we do not offer
add "number of people/pets greater then 5" because seller product base cost only covers up to 5 drawings.
See Examples Here