If you are using last touch channel attribution, then the credit for the conversion will be given to the last channel that the user interacted with before making the conversion.
In your example, if the user visited your website first through a paid search and then later through an organic search (SEO), and then made a conversion, the credit for the conversion will be given to the organic search channel (SEO) since it was the last channel the user interacted with before making the conversion.
Therefore, in the context of last touch channel attribution, the first visit from Paid search will not be counted in this particular conversion event.