Can the “Commerce Products”-field allow for selection of variants?
At the moment there is no Commerce variants field type unfortunately.   It comes up a lot, someone should post it here: https://github.com/craftcms/commerce/issues. 

Edit - I've gone ahead and posted this here - https://github.com/craftcms/commerce/issues

In the meantime yes a text or eg table field could store variant IDs...which I suppose is ultimately what a proper field type would do basically.