I have several keywords with "Low search volume", no impressions or clicks. My campaign has only one ad group.
Are these keywords effecting the campaign in any way?
Generally No, it shouldn't have any impact on campaign performance.
If they are not getting impressions then you can pause or delete to make your campaign look clean.
If you are thinking to build high performing campaign then you may need to have more than one campaign and few ad groups and the best practice is, you should structure your campaign based on your website structure.
If the keyword is not relevant to the ad group and landing page then it is best to create new and more relevant ad group+ad